HOME plateWON | World!OfNumbers Palindromic Quasi_Over_Squaresof the form n^2+(n+x) n(n+0) n(n+1) n(n+2) n(n+x) n^2+1 n^2+x n^2–x n^2+(n+1)

Introduction

Palindromic numbers are numbers which read the same from
left to right (forwards) as from the right to left (backwards)
Here are a few random examples : 7, 3113, 44611644

Quasi_Over_Square numbers are defined and calculated by this extraordinary intricate and excruciatingly complex formula.
So, this line is for experts only

 base2 + ( base + X )

 PLAIN TEXT QUASIMOR

Palindromic Quasi_Over_Squares

Quasi_Over_Squares of the form x2 + (x + 0) can only end with a 0, 2 or 6. And if it terminates in 6, it terminates in 06 or 56 only.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.
Main source see Palindromic Pronic Numbers
2 can be followed by any number : 20, 21, 22, 23, 24, 25, 26, 27, 28 or 29
6 can only be followed by 0 or 5 : 60 or 65

Quasi_Over_Squares of the form x2 + (x + 1) can only end with a 1, 3 or 7. And if it terminates in 7, it terminates in 07 or 57 only.
Even length palindromes of this form are not possible as never divisible by 11.
Main source see Palindromic Quasi-Over-Squares
1 can be followed by any number : 10, 11, 12, 13, 14, 15, 16, 17, 18 or 19
3 can be followed by any number : 30, 31, 32, 33, 34, 35, 36, 37, 38 or 39
7 can only be followed by 0 or 5 : 70 or 75

Quasi_Over_Squares of the form x2 + (x + 2) can only end with a 2, 4 or 8. And if it terminates in 8, it terminates in 08 or 58 only.
2 can be followed by any number : 20, 21, 22, 23, 24, 25, 26, 27, 28 or 29
4 can be followed by any number : 40, 41, 42, 43, 44, 45, 46, 47, 48 or 49
8 can only be followed by 0 or 5 : 80 or 85
There are no palindromic Quasi_Over_Squares of type x^2 + (x+2) of lengths 8, 14, 28, 34, 38, 48, 52, 54.

Quasi_Over_Squares of the form x2 + (x + 3) can only end with a 3, 5 or 9. And if it terminates in 9, it terminates in 09 or 59 only.
3 can be followed by any number : 30, 31, 32, 33, 34, 35, 36, 37, 38 or 39
5 can be followed by any number : 50, 51, 52, 53, 54, 55, 56, 57, 58 or 59
9 can only be followed by 0 or 5 : 90 or 95 { This 90... produces ever expanding Mandelbrot-like infinite palindromes }.
There are no palindromic Quasi_Over_Squares of type x^2 + (x+3) of lengths 20, 24, 28, 30, 32, 34, 36, 44, 52, 54.

Quasi_Over_Squares of the form x2 + (x + 4) can only end with a 0, 4 or 6. And if it terminates in 0, it terminates in 10 or 60 only.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.
Even length palindromes of this form are not possible as never divisible by 11.
4 can be followed by any number : 40, 41, 42, 43, 44, 45, 46, 47, 48 or 49
6 can be followed by any number : 60, 61, 62, 63, 64, 65, 66, 67, 68 or 69
There are no palindromic Quasi_Over_Squares of type x^2 + (x+4) of EVEN length.

Quasi_Over_Squares of the form x2 + (x + 5) can only end with a 1, 5 or 7. And if it terminates in 1, it terminates in 11 or 61 only.
1 can only be followed by 1 or 6 : 11 or 16
5 can be followed by any number : 50, 51, 52, 53, 54, 55, 56, 57, 58 or 59
7 can be followed by any number : 70, 71, 72, 73, 74, 75, 76, 77, 78 or 79
There are no palindromic Quasi_Over_Squares of type x^2 + (x+5) of lengths 6, 10, 12, 15, 18, 26, 28, 40, 42, 48, 49, {51 up to 54}.

Quasi_Over_Squares of the form x2 + (x + 6) can only end with a 2, 6 or 8. And if it terminates in 2, it terminates in 12 or 62 only.
Even length palindromes of this form are not possible as never divisible by 11.
2 can only be followed by 1 or 6 : 21 or 26
6 can be followed by any number : 60, 61, 62, 63, 64, 65, 66, 67, 68 or 69
8 can be followed by any number : 80, 81, 82, 83, 84, 85, 86, 87, 88 or 89
There are no palindromic Quasi_Over_Squares of type x^2 + (x+6) of EVEN length nor of length 31.

Quasi_Over_Squares of the form x2 + (x + 7) can only end with a 3, 7 or 9. And if it terminates in 3, it terminates in 13 or 63 only.
Even length palindromes of this form are not possible as never divisible by 11.
3 can only be followed by 1 or 6 : 31 or 36
7 can be followed by any number : 70, 71, 72, 73, 74, 75, 76, 77, 78 or 79
9 can be followed by any number : 90, 91, 92, 93, 94, 95, 96, 97, 98 or 99
There are no palindromic Quasi_Over_Squares of type x^2 + (x+7) of EVEN length.

Quasi_Over_Squares of the form x2 + (x + 8) can only end with a 0, 4 or 8. And if it terminates in 4, it terminates in 14 or 64 only.
Alas, my palindromes may not have leading zero's! So the zero option must not be investigated.
Even length palindromes of this form are not possible as never divisible by 11.
4 can only be followed by 1 or 6 : 41 or 46
8 can be followed by any number : 80, 81, 82, 83, 84, 85, 86, 87, 88 or 89
There are no palindromic Quasi_Over_Squares of type x^2 + (x+8) of EVEN length nor of lengths 15, 21, 25, 45, 47.

Quasi_Over_Squares of the form x2 + (x + 9) can only end with a 1, 5 or 9. And if it terminates in 5, it terminates in 15 or 65 only.
1 can be followed by any number : 10, 11, 12, 13, 14, 15, 16, 17, 18 or 19
5 can only be followed by 1 or 6 : 51 or 56
9 can be followed by any number : 90, 91, 92, 93, 94, 95, 96, 97, 98 or 99
There are no palindromic Quasi_Over_Squares of type x^2 + (x+9) of lengths 20, 22, 34.

 Quasi_Over_Squares Change of variables CUDApalin parameters Base Correction x^2 + (x+0) n.a. `A B C →  1 1 0 ` base = CUDAbase x^2 + (x+1) n.a. `A B C →  1 1 1 ` base = CUDAbase x^2 + (x+2) n.a. `A B C →  1 1 2 ` base = CUDAbase x^2 + (x+3) n.a. `A B C →  1 1 3 ` base = CUDAbase x^2 + (x+4) n.a. `A B C →  1 1 4 ` base = CUDAbase x^2 + (x+5) n.a. `A B C →  1 1 5 ` base = CUDAbase x^2 + (x+6) n.a. `A B C →  1 1 6 ` base = CUDAbase x^2 + (x+7) n.a. `A B C →  1 1 7 ` base = CUDAbase x^2 + (x+8) n.a. `A B C →  1 1 8 ` base = CUDAbase x^2 + (x+9) n.a. `A B C →  1 1 9 ` base = CUDAbase

Some people regard 1997 as a bad year !

So does Vincent Prosper because he figured out that after applying the "add & reverse" procedure to 1997,
this yearnumber never transformed into a palindrome. Follow this link to arrive at his website.

As for me, 1997 is a lucky year because of the following relations with the number of the beast 666 and other various palindromic numbers :

14132 + ( 1413 + 9 ) = 1997991 or from the right 1997991.
Note that 1413 = 666 + 747

300032 + ( 30003 + 1997 ) = 900212009.
Note that 1997 = 666 + 1331
and moreover 1331 = 113 is a palindromic cube !

An infinite palindromic pattern resides in the list for case n^2 + (n + 2)

212 + 23 = 464
2012 + 203 = 40604
20012 + 2003 = 4006004
200012 + 20003 = 400060004
2000012 + 200003 = 40000600004
20000012 + 2000003 = 4000006000004
200000012 + 20000003 = 400000060000004

Some (in)finite palindromic pattern resides in the list for case n^2 + (n + 3)

1._
(QM3) 3009819902 [9059015845485109509] {L=19}
(QM3) 30009981999002 [900599019580454085910995009] {L=27}
(QM3) 300009998199990002 [90005999019958004540085991099950009] {L=35}
(QM3) 3000009999819999900002 [9000059999019995800045400085999109999500009] {L=43}
(QM3) 30000009999981999999000002 [900000599999019999580000454000085999910999995000009] {L=51}

2._
(QM3) 300990099009902 [90595039701990909910793059509] {L=29}
(QM3) 30009900990099002 [900594157435545090545534751495009] {L=33}
(QM3) 3000099009900990002 [9000594069208900509050098029604950009] {L=37}
(QM3) 300000990099009900002 [is no longer palindromic] {L=41}

An infinite palindromic pattern hides in the list for case n^2 + (n + 4)

202 + 24 = 424
2002 + 204 = 40204
20002 + 2004 = 4002004
200002 + 20004 = 400020004
2000002 + 200004 = 40000200004
20000002 + 2000004 = 4000002000004
200000002 + 20000004 = 400000020000004

A very nice but finite palindromic pattern hides in the list for case n^2 + (n + 6)

282 + 34 = 818
2882 + 294 = 83238
28882 + 2894 = 8343438
288882 + 28894 = 834545438
2888882 + 288894 = 83456565438
28888882 + 2888894 = 8345676765438
288888882 + 28888894 = 834567878765438
2888888882 + 288888894 = 83456789898765438
alas
28888888882 + 2888888894 = 8345679010098765438
is no longer palindromic !

An infinite palindromic pattern hides in the list for case n^2 + (n + 7)

312 + 38 = 999
3012 + 308 = 90909
30012 + 3008 = 9009009
300012 + 30008 = 900090009
3000012 + 300008 = 90000900009
30000012 + 3000008 = 9000009000009
300000012 + 30000008 = 900000090000009

A second peculiar infinite palindromic pattern emerges as well.

3121_{00}_1208 = 9740648543458460479 which is basically a compressed form of 974064[1 + 7]54345[7 + 1]460479

3121_{000}_1208 = 9740641_{}_7543457_{}_1460479
3121_{0000}_1208 = 9740641_{0}_7543457_{0}_1460479
3121_{00000}_1208 = 9740641_{00}_7543457_{00}_1460479
or generally
3121_{0}n _1208 = 9740641_{0}n-3 _7543457_{0}n-3 _1460479 ( for n>=3 )

An infinite palindromic pattern hides in the list for case n^2 + (n + 9)

302 + 39 = 939
3002 + 309 = 90309
30002 + 3009 = 9003009
300002 + 30009 = 900030009
3000002 + 300009 = 90000300009
30000002 + 3000009 = 9000003000009
300000002 + 30000009 = 900000030000009

The Table

Index NrBasenumberLength
Palindromic Quasi_Over_Squares of form n^2+(n+X)Length

[QP1] Case X = 0  [Scanned exhaustively up to length 59]
See in-depth webpage about Palindromic Pronic Numbers

[QM1] Case X = 1  [Scanned exhaustively up to length 53]
See in-depth webpage about Palindromic Quasi-Over-Squares

[QM2] Case X = 2
One can find the regular numbers of the form n2+(n+2) at
%N n^2 + (n+2). under A014206.
The palindromic numbers of the form n2+(n+2) are categorised as follows :
%N n^2 + (n+2) is a palindrome. under A027712.
%N Palindromes of the form n^2 + (n+2). under A027713.

More terms from Giovanni Resta, Aug 28, 2018. See Index Nrs 51 up to 65.
More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 66 up to 115.
More terms from Robert Xiao, Nov 3, 2022. See Index Nrs 116 up to 121.
More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 122 up to 128.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 129 up to 152.
More terms from Patrick De Geest, Jun 21, 2023. See Index Nrs 153 up to 155.
More terms from Patrick De Geest, Jul 18, 2023. See Index Nrs 156 up to 161.
1612.916.941.228.048.406.027.740.141.83228
8.508.546.127.888.543.060.000.205.907.095.020.000.603.458.887.216.458.05855
1602.105.878.593.908.461.957.725.397.98128
4.434.724.652.281.880.828.482.876.291.926.782.848.280.881.822.564.274.34455
1592.000.000.000.000.000.000.000.000.00128
4.000.000.000.000.000.000.000.000.006.000.000.000.000.000.000.000.000.00455
1581.590.449.007.023.765.386.552.303.24928
2.529.528.043.942.881.319.886.728.507.058.276.889.131.882.493.408.259.25255
1571.489.727.359.201.790.342.383.089.27928
2.219.287.604.754.340.068.700.850.059.500.580.078.600.434.574.067.829.12255
1561.483.733.601.665.779.326.753.416.62028
2.201.465.400.712.105.517.353.667.074.707.663.537.155.012.170.045.641.02255
155291.819.736.041.306.538.408.058.18727
85.158.758.343.217.822.268.333.031.213.033.386.222.871.234.385.785.15853
154208.232.426.734.519.414.742.680.58827
43.360.743.543.746.995.891.455.860.006.855.419.859.964.734.534.706.33453
153200.000.000.000.000.000.000.000.00127
40.000.000.000.000.000.000.000.000.600.000.000.000.000.000.000.000.00453
152149.374.451.201.321.447.016.114.92027
22.312.726.671.695.962.285.645.833.833.854.658.226.959.617.662.721.32253
15120.184.103.716.273.036.994.718.97326
407.398.042.829.267.022.695.499.959.994.596.220.762.928.240.893.70451
15020.000.000.000.000.000.000.000.00126
400.000.000.000.000.000.000.000.060.000.000.000.000.000.000.000.00451
14916.950.149.078.625.980.485.603.75526
287.307.553.787.645.175.186.196.828.691.681.571.546.787.355.703.78251
1488.973.684.520.672.509.625.913.62225
80.527.013.876.557.408.839.676.399.367.693.880.475.567.831.072.50850
1472.920.302.583.592.557.260.579.15225
8.528.167.179.737.364.886.640.530.350.466.884.637.379.717.618.25849
1462.153.012.016.959.597.668.794.32125
4.635.460.745.172.434.879.800.352.530.089.784.342.715.470.645.36449
1452.074.849.351.833.902.559.760.68825
4.304.999.832.805.565.571.528.799.978.251.755.655.082.389.994.03449
1442.000.000.000.000.000.000.000.00125
4.000.000.000.000.000.000.000.006.000.000.000.000.000.000.000.00449
1431.650.258.386.595.090.091.043.62925
2.723.352.742.527.429.822.694.638.364.962.289.247.252.472.533.27249
1421.637.749.528.521.602.840.444.73925
2.682.223.518.172.732.395.755.732.375.575.932.372.718.153.222.86249
1411.626.164.912.369.999.442.359.23525
2.644.412.322.223.327.965.385.210.125.835.697.233.222.232.144.46249
1401.581.919.878.671.183.336.539.55025
2.502.470.502.535.051.408.159.044.409.518.041.505.352.050.742.05249
1391.580.455.679.910.094.737.787.65925
2.497.840.156.160.079.835.357.317.137.535.389.700.616.510.487.94249
138221.912.986.021.509.668.199.13124
49.245.373.364.982.745.396.339.693.369.354.728.946.337.354.29447
137208.498.909.605.413.220.335.11124
43.471.795.306.646.273.234.619.891.643.237.264.660.359.717.43447
136200.000.000.000.000.000.000.00124
40.000.000.000.000.000.000.000.600.000.000.000.000.000.000.00447
135169.034.548.441.728.779.604.81924
28.572.678.566.899.153.393.308.880.339.335.199.866.587.627.58247
13467.230.171.214.418.445.395.55123
4.519.895.921.520.018.544.969.449.694.458.100.251.295.989.15446
13364.231.123.411.050.024.609.22823
4.125.637.214.645.538.548.618.888.168.458.355.464.127.365.21446
13247.060.003.163.260.717.494.90423
2.214.643.897.726.108.736.838.778.386.378.016.277.983.464.12246
13128.340.760.432.776.860.355.25723
803.198.701.908.050.453.059.545.950.354.050.809.107.891.30845
13021.013.528.000.013.139.582.70623
441.568.359.007.336.217.978.222.879.712.633.700.953.865.14445
12920.000.000.000.000.000.000.00123
400.000.000.000.000.000.000.060.000.000.000.000.000.000.00445
1284.757.677.656.778.346.810.40422
22.635.496.685.807.900.793.566.539.700.970.858.669.453.62244
1274.715.988.110.384.558.673.80422
22.240.543.857.288.520.366.666.666.302.588.275.834.504.22244
1262.838.747.628.261.247.913.57722
8.058.488.096.958.860.174.044.404.710.688.596.908.848.50843
1252.000.000.000.000.000.000.00122
4.000.000.000.000.000.000.006.000.000.000.000.000.000.00443
1241.614.610.539.612.041.804.46022
2.606.967.194.626.288.816.955.596.188.826.264.917.696.06243
123642.382.560.558.903.872.22821
412.655.354.110.213.800.784.487.008.312.011.453.556.21442
122527.378.686.600.101.977.84521
278.128.279.080.048.581.444.444.185.840.080.972.821.87242
121221.301.942.040.661.354.53821
48.974.549.550.968.237.449.094.473.286.905.594.547.98441
120207.569.859.046.680.002.06321
43.085.246.384.658.603.895.059.830.685.648.364.258.03441
119200.000.000.000.000.000.00121
40.000.000.000.000.000.000.600.000.000.000.000.000.00441
118165.711.647.551.849.788.44521
27.460.350.134.348.483.984.348.938.484.343.105.306.47241
11767.656.578.638.660.502.37620
4.577.412.633.089.252.596.996.952.529.803.362.147.75440
11645.435.227.161.435.625.39920
2.064.359.867.211.257.597.887.957.521.127.689.534.60240
11522.349.935.885.854.845.65620
499.519.634.101.822.224.454.422.228.101.436.915.99439
11421.648.788.975.466.017.94620
468.670.064.104.258.998.989.899.852.401.460.076.86439
11320.000.000.000.000.000.00120
400.000.000.000.000.000.060.000.000.000.000.000.00439
11215.682.422.422.343.540.31520
245.938.373.032.823.434.777.434.328.230.373.839.54239
11115.647.015.327.334.577.78420
244.829.088.653.843.204.373.402.348.356.880.928.44239
11014.681.808.231.390.847.41020
215.555.492.943.336.042.818.240.633.349.294.555.51239
10914.468.011.600.019.886.09920
209.323.359.658.309.984.636.489.903.856.953.323.90239
108Prime!    2.837.459.270.361.355.69719
8.051.175.110.959.597.047.407.959.590.115.711.50837
1072.058.677.547.772.551.63319
4.238.153.245.702.806.613.166.082.075.423.518.32437
1062.000.000.000.000.000.00119
4.000.000.000.000.000.006.000.000.000.000.000.00437
1051.604.777.671.384.426.74919
2.575.311.374.574.023.168.613.204.754.731.135.75237
1041.472.063.339.927.111.61419
2.166.970.476.757.362.959.592.637.576.740.796.61237
103703.359.338.401.854.46818
494.714.358.917.094.430.034.490.719.853.417.49436
102664.384.175.944.617.41818
441.406.333.245.608.354.453.806.542.333.604.14436
101468.033.494.872.988.31418
219.055.352.323.023.578.875.320.323.253.550.91236
100200.000.000.000.000.00118
40.000.000.000.000.000.600.000.000.000.000.00435
9920.548.848.021.323.33317
422.255.155.003.443.878.344.300.551.552.22433
9820.000.000.000.000.00117
400.000.000.000.000.060.000.000.000.000.00433
976.850.109.083.855.64616
46.923.994.460.721.644.612.706.449.932.96432
964.514.881.483.507.32416
20.384.154.810.117.299.271.101.845.148.30232
952.916.449.084.541.63216
8.505.675.262.723.726.273.272.625.765.05831
942.829.855.733.529.60216
8.008.083.472.590.364.630.952.743.808.00831
932.188.234.330.424.21616
4.788.369.484.847.119.117.484.849.638.87431
922.067.032.967.032.95816
4.272.625.286.801.075.701.086.825.262.72431
912.000.000.000.000.00116
4.000.000.000.000.006.000.000.000.000.00431
901.572.610.479.725.85916
2.473.103.720.943.597.953.490.273.013.74231
891.542.828.488.662.80516
2.380.319.745.429.556.559.245.479.130.83231
881.488.667.854.682.27916
2.216.131.981.564.340.434.651.891.316.12231
87925.624.837.663.11215
856.781.340.098.863.368.890.043.187.65830
86222.473.255.490.46815
49.494.349.408.527.272.580.494.349.49429
85210.516.022.946.98115
44.316.995.917.414.041.471.959.961.34429
84200.000.000.000.00115
40.000.000.000.000.600.000.000.000.00429
8320.000.000.000.00114
400.000.000.000.060.000.000.000.00427
8214.754.699.832.48514
217.701.167.146.747.641.761.107.71227
815.270.176.390.87013
27.774.759.190.888.809.195.747.77226
804.904.746.291.44013
24.056.536.183.399.338.163.565.04226
792.925.116.099.26713
8.556.304.194.193.914.914.036.55825
782.838.046.790.77713
8.054.509.586.642.466.859.054.50825
772.084.206.947.11113
4.343.918.598.387.838.958.193.43425
762.071.648.052.43313
4.291.725.653.151.513.565.271.92425
752.067.032.967.04113
4.272.625.286.836.386.825.262.72425
742.015.098.740.20113
4.060.622.932.761.672.392.260.60425
732.000.000.000.00113
4.000.000.000.006.000.000.000.00425
721.644.864.716.95413
2.705.579.937.081.807.399.755.07225
711.549.917.788.44013
2.402.245.150.924.290.515.422.04225
701.511.192.351.79513
2.283.702.324.125.214.232.073.82225
69Prime!    899.201.757.55712
808.563.800.794.497.008.365.80824
68Prime!    684.374.223.05312
468.368.077.180.081.770.863.86424
67675.835.699.32312
456.753.892.480.084.298.357.65424
66654.264.529.13312
428.062.074.082.280.470.260.82424
65544.298.466.46512
296.260.820.596.695.028.062.69224
64200.000.000.00112
40.000.000.000.600.000.000.00423
63146.078.456.08512
21.338.915.332.323.351.983.31223
6289.921.234.44211
8.085.828.403.663.048.285.80822
6148.973.960.09411
2.398.448.767.337.678.448.93222
6048.762.480.70511
2.377.779.524.554.259.777.73222
5947.382.584.97911
2.245.109.359.339.539.015.42222
5820.000.000.00111
400.000.000.060.000.000.00421
576.383.911.90110
40.754.331.166.113.345.70420
562.916.938.79210
8.508.531.919.191.358.05819
552.137.594.67610
4.569.311.001.001.139.65419
542.092.486.16310
4.378.498.344.438.948.73419
53Prime!    2.089.713.86310
4.366.904.031.304.096.63419
522.069.010.86610
4.280.805.965.695.080.82419
512.067.032.95810
4.272.625.251.525.262.72419
502.000.000.00110
4.000.000.006.000.000.00419
491.553.608.45910
2.413.699.245.429.963.14219
481.434.631.49910
2.058.167.539.357.618.50219
47528.342.9299
279.146.251.152.641.97218
46482.441.6699
232.749.964.469.947.23218
45223.314.9569
49.869.569.796.596.89417
44213.934.6239
45.768.023.132.086.75417
43200.000.0019
40.000.000.600.000.00417
42161.280.5399
26.011.412.421.411.06217
4192.610.8528
8.576.770.000.776.75816
4048.829.9308
2.384.362.112.634.83216
3929.287.0528
857.731.444.137.75815
3822.012.0388
484.529.838.925.48415
3721.855.1088
477.645.767.546.77415
3621.147.9068
447.233.949.332.74415
3520.000.0018
400.000.060.000.00415
3417.101.8098
292.471.888.174.29215
3314.842.9958
220.314.515.413.02215
322.000.0017
4.000.006.000.00413
311.651.7547
2.728.292.928.27213
301.620.6607
2.626.540.456.26213
29501.4746
251.476.674.15212
28Prime!    219.0836
47.997.579.97411
27200.0016
40.000.600.00411
2689.7775
8.059.999.50810
2528.3775
805.282.5089
2420.9935
440.727.0449
2320.0015
400.060.0049
2216.7805
281.585.1829
212.1834
4.767.6747
202.1064
4.437.3447
192.0014
4.006.0047
181.6544
2.737.3727
171.5304
2.342.4327
161.4244
2.029.2027
158973
805.5086
14Prime!    4793
229.9226
132923
85.5585
122033
41.4145
112013
40.6045
10922
8.5584
9502
2.5524
8212
4643
7152
2423
6142
2123
561
442
441
222
3Prime!    21
81
211
41
101
Prime!    21

[QM3] Case X = 3
One can find the regular numbers of the form n2+(n+3) at
%N n^2 + (n+3). under A027688.
The palindromic numbers of the form n2+(n+3) are categorised as follows :
%N n^2 + (n+3) is a palindrome. under A027714.
%N Palindromes of the form n^2 + (n+3). under A027715.

More terms from Giovanni Resta, Aug 29, 2018. See Index Nrs 38 up to 50.
More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 51 up to 124.
More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 126 up to 188
except Nr 167 which was already known.
More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 189 up to 316
except Nr 286 which was already known.
More terms from Patrick De Geest, Jun 22, 2023. See Index Nrs 317 up to 352
More terms from Patrick De Geest, Jul 18, 2023. See Index Nrs 353 up to 392
392 3.000.999.009.990.090.099.900.999.002 9.005.995.057.961.500.899.227.496.415.146.947.229.980.051.697.505.995.009 3.000.999.009.900.999.009.900.999.002 9.005.995.057.426.776.353.457.557.605.067.557.543.536.776.247.505.995.009 3.000.999.009.900.909.009.900.999.002 9.005.995.057.426.236.173.635.775.433.345.775.363.716.326.247.505.995.009 3.000.999.009.900.090.009.900.999.002 9.005.995.057.421.320.537.257.558.415.148.557.527.350.231.247.505.995.009 3.000.990.999.009.909.900.999.099.002 9.005.946.976.138.497.048.398.652.633.362.568.938.407.948.316.796.495.009 3.000.990.990.009.000.900.099.099.002 9.005.946.922.115.203.340.198.653.443.443.568.910.433.025.112.296.495.009 3.000.990.099.099.909.990.990.099.002 9.005.941.574.895.687.588.514.914.633.364.194.158.857.865.984.751.495.009 3.000.990.099.099.000.990.990.099.002 9.005.941.574.890.231.788.514.751.823.281.574.158.871.320.984.751.495.009 3.000.990.099.009.090.900.990.099.002 9.005.941.574.350.593.208.724.635.451.545.364.278.023.950.534.751.495.009 3.000.990.090.099.909.990.090.099.002 9.005.941.520.877.865.880.314.752.633.362.574.130.885.687.780.251.495.009 3.000.900.900.090.999.090.009.009.002 9.005.406.212.166.968.502.222.713.081.803.172.222.058.696.612.126.045.009 3.000.099.990.000.999.000.099.990.002 9.000.599.950.003.994.300.379.981.009.001.899.730.034.993.000.599.950.009 3.000.099.909.999.000.999.909.990.002 9.000.599.469.976.013.899.839.743.027.203.479.389.983.106.799.649.950.009 3.000.099.900.999.909.999.009.990.002 9.000.599.415.979.669.777.077.562.217.122.657.707.779.669.795.149.950.009 3.000.099.900.999.819.999.009.990.002 9.000.599.415.979.129.759.095.382.241.422.835.909.579.219.795.149.950.009 3.000.099.900.999.000.999.009.990.002 9.000.599.415.974.215.595.457.545.207.025.457.545.955.124.795.149.950.009 3.000.099.900.099.909.990.009.990.002 9.000.599.410.579.489.902.085.926.017.106.295.802.099.849.750.149.950.009 3.000.099.900.099.000.990.009.990.002 9.000.599.410.574.035.720.467.545.207.025.457.640.275.304.750.149.950.009 3.000.099.000.999.000.999.000.990.002 9.000.594.015.795.203.797.201.745.207.025.471.027.973.025.975.104.950.009 3.000.099.000.099.000.990.000.990.002 9.000.594.010.395.025.542.211.761.407.041.671.122.455.205.930.104.950.009 3.000.090.009.900.999.009.900.090.002 9.000.540.067.507.776.337.252.103.425.243.012.527.336.777.057.600.450.009 3.000.090.009.900.090.009.900.090.002 9.000.540.067.502.322.173.614.104.235.324.014.163.712.232.057.600.450.009 3.000.090.009.000.090.000.900.090.002 9.000.540.062.102.160.102.602.322.055.502.232.062.010.612.012.600.450.009 3.000.090.000.900.090.009.000.090.002 9.000.540.013.500.702.071.012.322.055.502.232.101.702.070.053.100.450.009 3.000.009.999.900.999.009.999.900.002 9.000.059.999.505.992.079.989.401.209.021.049.899.702.995.059.999.500.009 3.000.009.999.009.999.900.999.900.002 9.000.059.994.159.979.606.977.520.209.020.257.796.069.799.514.999.500.009 3.000.009.999.000.999.000.999.900.002 9.000.059.994.105.974.026.977.423.009.003.247.796.204.795.014.999.500.009 3.000.009.999.000.090.000.999.900.002 9.000.059.994.100.520.008.799.240.019.100.429.978.000.250.014.999.500.009 3.000.009.990.009.999.900.099.900.002 9.000.059.940.159.799.700.397.504.009.004.057.930.079.979.510.499.500.009 3.000.009.990.000.999.000.099.900.002 9.000.059.940.105.794.120.559.423.009.003.249.550.214.975.010.499.500.009 3.000.009.990.000.180.000.099.900.002 9.000.059.940.100.880.104.195.802.043.402.085.914.010.880.010.499.500.009 3.000.009.990.000.090.000.099.900.002 9.000.059.940.100.340.102.397.602.019.102.067.932.010.430.010.499.500.009 3.000.009.000.099.000.990.000.900.002 9.000.054.000.675.007.722.033.021.227.221.203.302.277.005.760.004.500.009 3.000.009.000.090.000.090.000.900.002 9.000.054.000.621.002.160.015.120.047.400.215.100.612.001.260.004.500.009 3.000.000.999.000.999.000.999.000.002 9.000.005.994.006.992.008.990.005.009.005.000.998.002.996.004.995.000.009 3.000.000.990.000.999.000.099.000.002 9.000.005.940.006.974.102.572.021.209.021.202.752.014.796.000.495.000.009 3.000.000.990.000.090.000.099.000.002 9.000.005.940.001.520.100.772.200.219.120.022.770.010.251.000.495.000.009 3.000.000.900.000.090.000.009.000.002 9.000.005.400.001.350.000.216.000.039.300.006.120.000.531.000.045.000.009 2.343.633.080.809.476.929.100.713.306 5.492.616.017.464.520.217.729.745.612.165.479.277.120.254.647.106.162.945 1.743.330.003.962.878.046.838.570.699 3.039.199.502.717.208.386.494.573.329.233.754.946.838.027.172.059.919.303 Prime!    300.990.099.099.090.900.900.990.097 Prime!    90.595.039.755.680.561.154.195.403.930.459.145.116.508.655.793.059.509 300.099.909.990.099.009.990.999.002 90.059.955.976.065.527.578.873.832.523.837.887.572.556.067.955.995.009 300.099.900.999.009.900.099.000.997 90.059.950.579.615.543.235.461.159.395.116.453.234.551.697.505.995.009 300.099.900.990.009.990.099.000.997 90.059.950.574.213.799.035.542.159.395.124.553.099.731.247.505.995.009 300.099.900.099.009.900.999.000.997 90.059.950.039.435.722.787.423.159.395.132.478.722.753.493.005.995.009 300.099.099.909.900.990.999.099.002 90.059.469.766.732.736.983.993.254.345.239.938.963.723.766.796.495.009 300.099.099.009.900.990.099.099.002 90.059.469.226.554.357.415.993.092.329.039.951.475.345.562.296.495.009 300.099.009.900.909.099.009.900.997 90.059.415.743.505.937.435.545.545.754.554.553.473.950.534.751.495.009 300.099.000.990.990.090.099.900.997 90.059.410.395.790.271.079.841.737.573.714.897.017.209.759.301.495.009 300.099.000.990.099.009.900.099.002 90.059.410.395.255.446.524.315.670.507.651.342.564.455.259.301.495.009 300.009.999.099.990.000.900.009.997 90.005.999.559.976.001.150.041.997.179.914.005.110.067.995.599.950.009 300.009.999.009.990.009.900.009.997 90.005.999.505.974.206.720.323.779.197.732.302.760.247.950.599.950.009 300.009.999.000.999.900.099.990.002 90.005.999.500.579.961.055.997.200.900.279.955.016.997.500.599.950.009 300.009.999.000.099.000.099.990.002 90.005.999.500.039.403.039.798.010.901.089.793.030.493.000.599.950.009 300.009.990.999.900.999.909.990.002 90.005.994.699.760.678.967.774.212.721.247.776.987.606.799.649.950.009 300.009.990.099.900.999.009.990.002 90.005.994.159.742.695.437.934.430.703.443.973.459.624.795.149.950.009 300.009.990.099.000.099.009.990.002 90.005.994.159.202.137.437.773.240.704.237.773.473.120.295.149.950.009 300.009.990.009.990.009.990.009.997 90.005.994.105.794.305.594.505.399.199.350.549.550.349.750.149.950.009 300.009.990.009.909.009.990.009.997 90.005.994.105.745.703.976.123.787.378.732.167.930.754.750.149.950.009 300.009.990.000.990.099.990.009.997 Prime!    90.005.994.100.394.179.776.204.779.197.740.267.797.149.300.149.950.009 300.009.900.999.900.999.900.990.002 90.005.940.697.970.398.980.194.050.705.049.108.989.307.979.604.950.009 300.009.900.999.009.900.099.009.997 90.005.940.697.435.721.453.448.739.393.784.435.412.753.479.604.950.009 300.009.900.990.009.990.099.009.997 90.005.940.692.035.597.237.329.739.393.792.373.279.553.029.604.950.009 300.009.900.099.900.999.000.990.002 90.005.940.157.952.577.450.354.430.703.445.305.477.525.975.104.950.009 300.009.900.099.000.099.000.990.002 90.005.940.157.412.019.612.355.240.704.255.321.691.021.475.104.950.009 300.009.900.009.900.990.000.990.002 90.005.940.103.950.790.040.294.050.705.049.204.009.705.930.104.950.009 300.009.900.009.000.090.000.990.002 90.005.940.103.410.232.202.457.022.722.075.420.223.201.430.104.950.009 300.000.999.990.999.909.999.900.002 90.000.599.995.599.927.999.841.002.920.014.899.972.999.559.999.500.009 300.000.999.009.990.009.900.099.997 90.000.599.406.992.026.900.199.579.197.599.100.962.029.960.499.500.009 300.000.999.000.999.900.099.900.002 90.000.599.401.597.943.057.741.400.900.414.775.034.979.510.499.500.009 300.000.999.000.099.000.099.900.002 90.000.599.401.057.401.257.742.210.901.224.775.210.475.010.499.500.009 300.000.990.009.990.009.990.099.997 90.000.594.006.974.125.774.379.579.197.597.347.752.147.960.049.500.009 300.000.990.000.099.000.009.900.002 900.00.594.001.039.500.201.960.030.903.006.910.200.593.010.049.500.009 300.000.099.000.099.000.099.000.002 90.000.059.400.069.201.079.002.030.903.020.097.010.296.000.495.000.009 300.000.090.000.099.000.009.000.002 90.000.054.000.067.500.023.220.012.921.002.232.000.576.000.045.000.009 240.781.061.176.902.353.671.153.083 57.975.519.421.475.193.851.969.411.811.496.915.839.157.412.491.557.975 30.838.426.999.727.240.504.327.987 951.008.579.817.506.052.408.398.050.893.804.250.605.718.975.800.159 30.009.990.999.009.009.990.999.002 900.599.559.760.601.797.498.562.353.265.894.797.106.067.955.995.009 30.009.990.990.099.900.990.999.002 900.599.559.225.877.235.779.554.252.455.977.532.778.522.955.995.009 30.009.990.009.900.099.000.999.002 900.599.500.394.303.744.135.992.070.299.531.447.303.493.005.995.009 30.009.900.999.099.909.990.099.002 900.594.157.975.777.775.824.374.252.473.428.577.777.579.751.495.009 30.009.900.999.090.909.990.099.002 900.594.157.975.237.597.606.390.535.093.606.795.732.579.751.495.009 30.009.900.999.009.009.990.099.002 900.594.157.970.321.975.822.746.151.647.228.579.123.079.751.495.009 30.009.900.990.099.900.990.099.002 900.594.157.435.599.017.743.358.050.853.347.710.995.534.751.495.009 30.009.900.990.009.000.990.099.002 900.594.157.430.143.217.743.366.151.663.347.712.341.034.751.495.009 30.009.900.900.909.090.090.099.002 900.594.152.082.384.217.026.912.717.219.620.712.483.280.251.495.009 30.009.900.099.099.909.900.099.002 900.594.103.957.956.782.042.754.252.457.240.287.659.759.301.495.009 30.009.900.099.009.009.900.099.002 900.594.103.952.500.982.204.746.151.647.402.289.005.259.301.495.009 30.009.900.090.099.900.900.099.002 900.594.103.417.778.040.161.754.252.457.161.040.877.714.301.495.009 30.009.900.090.009.000.900.099.002 900.594.103.412.322.240.325.382.353.283.523.042.223.214.301.495.009 30.006.690.109.888.660.569.252.802 900.401.451.350.889.956.509.102.474.201.905.659.988.053.154.104.009 30.000.999.900.099.900.099.990.002 900.059.995.005.794.215.779.630.090.036.977.512.497.500.599.950.009 30.000.999.900.009.000.099.990.002 900.059.995.000.340.033.997.800.191.008.799.330.043.000.599.950.009 30.000.999.000.099.900.009.990.002 900.059.941.003.995.200.199.630.090.036.991.002.599.300.149.950.009 30.000.990.099.990.999.900.990.002 900.059.406.979.757.986.237.404.171.404.732.689.757.979.604.950.009 30.000.990.099.981.999.900.990.002 900.059.406.979.217.968.415.604.414.406.514.869.712.979.604.950.009 30.000.990.009.990.999.000.990.002 900.059.401.579.579.722.337.242.171.242.733.227.975.975.104.950.009 30.000.990.009.981.999.000.990.002 900.059.401.579.039.704.517.062.414.260.715.407.930.975.104.950.009 30.000.990.009.909.099.000.990.002 900.059.401.574.665.560.173.612.353.216.371.065.566.475.104.950.009 30.000.990.009.900.099.000.990.002 900.059.401.574.125.542.353.434.070.434.353.245.521.475.104.950.009 30.000.099.900.999.990.099.900.002 900.005.994.069.979.615.793.022.090.220.397.516.979.960.499.500.009 30.000.099.900.099.900.099.900.002 900.005.994.015.974.035.954.050.090.050.459.530.479.510.499.500.009 30.000.099.900.009.000.099.900.002 900005994010520017.792.220.191.022.297.710.025.010.499.500.009 30.000.099.000.099.900.009.900.002 900.005.940.015.795.020.374.212.090.212.473.020.597.510.049.500.009 30.000.099.000.018.000.009.900.002 900.005.940.010.881.004.158.002.434.200.851.400.188.010.049.500.009 30.000.099.000.009.000.009.900.002 900.005.940.010.341.002.376.002.191.200.673.200.143.010.049.500.009 30.000.009.999.981.999.999.000.002 900.000.599.999.019.999.580.000.454.000.085.999.910.999.995.000.009 30.000.009.000.009.000.009.000.002 900.000.540.000.621.000.702.000.393.000.207.000.126.000.045.000.009 18.603.614.682.732.832.889.421.584 346.094.479.263.592.642.526.728.787.827.625.246.295.362.974.490.643 18.342.225.383.416.581.183.888.605 336.437.232.016.051.548.619.577.080.775.916.845.150.610.232.734.633 17.933.510.849.802.130.612.622.904 321.610.811.399.970.736.889.219.161.912.988.637.079.993.118.016.123 5.605.366.478.437.820.000.891.814 31.420.133.357.594.407.596.985.500.558.969.570.449.575.333.102.413 5.483.011.386.045.514.264.563.999 30.063.413.859.504.751.457.661.722.716.675.415.740.595.831.436.003 3.094.886.514.989.921.948.064.747 9.578.322.540.666.464.370.936.336.336.390.734.646.660.452.238.759 3.009.900.900.909.090.990.990.097 9.059.503.433.293.357.584.752.419.142.574.857.533.923.343.059.509 3.000.999.099.900.990.009.000.997 9.005.995.597.606.552.212.251.773.771.522.122.556.067.955.995.009 3.000.999.009.990.099.900.999.002 9.005.995.057.961.559.725.398.307.038.935.279.551.697.505.995.009 Prime!    3.000.999.009.900.990.099.000.997 9.005.995.057.426.722.870.253.393.933.520.782.276.247.505.995.009 3.000.999.009.000.999.099.000.997 9.005.995.052.024.978.671.223.773.773.221.768.794.202.505.995.009 3.000.999.000.990.099.000.999.002 9.005.995.003.943.572.224.778.307.038.774.222.753.493.005.995.009 3.000.990.990.099.009.900.900.997 9.005.946.922.655.435.741.059.175.719.501.475.345.562.296.495.009 3.000.990.990.009.099.900.900.997 9.005.946.922.115.797.541.227.655.567.221.457.975.112.296.495.009 3.000.990.099.909.090.009.900.997 9.005.941.579.752.370.039.451.855.581.549.300.732.579.751.495.009 3.000.990.099.009.900.990.099.002 9.005.941.574.355.455.347.514.905.094.157.435.545.534.751.495.009 Prime!    3.000.990.009.900.990.099.900.997 9.005.941.039.525.544.657.833.393.933.387.564.455.259.301.495.009 3.000.099.990.099.990.099.990.002 9.000.599.950.597.960.695.970.209.020.795.960.697.950.599.950.009 3.000.099.990.099.009.900.009.997 9.000.599.950.592.079.300.069.591.959.600.039.702.950.599.950.009 3.000.099.990.009.900.099.990.002 9.000.599.950.057.402.679.762.109.012.679.762.047.500.599.950.009 3.000.099.900.999.000.990.009.997 9.000.599.415.974.215.541.455.791.975.541.455.124.795.149.950.009 3.000.099.900.990.900.990.009.997 9.000.599.415.925.613.923.059.673.769.503.293.165.295.149.950.009 3.000.099.900.099.990.009.990.002 9.000.599.410.579.970.037.954.009.004.597.300.799.750.149.950.009 3.000.099.900.099.009.990.009.997 9.000.599.410.574.089.722.265.791.975.622.279.804.750.149.950.009 3.000.099.900.009.900.009.990.002 9.000.599.410.039.412.037.962.109.012.697.302.149.300.149.950.009 3.000.099.009.990.099.900.990.002 9.000.594.069.743.577.545.522.507.052.255.457.753.479.604.950.009 3.000.099.009.909.090.099.009.997 9.000.594.069.257.502.692.089.655.569.802.962.057.529.604.950.009 3.000.099.009.900.009.900.990.002 9.000.594.069.203.019.705.910.607.060.195.079.103.029.604.950.009 3.000.099.000.999.000.999.009.997 9.000.594.015.795.203.797.255.791.975.527.973.025.975.104.950.009 3.000.099.000.990.099.000.990.002 9.000.594.015.741.790.046.522.507.052.256.400.971.475.104.950.009 3.000.099.000.900.009.000.990.002 9.000.594.015.201.232.208.532.227.222.358.022.321.025.104.950.009 3.000.099.000.099.009.999.009.997 9.000.594.010.395.079.598.049.591.959.408.959.705.930.104.950.009 3.000.009.990.099.990.099.900.002 9.000.059.940.699.742.697.212.209.022.127.962.479.960.499.500.009 3.000.009.990.009.900.099.900.002 9.000.059.940.159.200.897.204.109.014.027.980.029.510.499.500.009 3.000.009.900.099.990.009.900.002 9.000.059.400.697.952.039.212.209.022.129.302.597.960.049.500.009 3.000.009.900.009.900.009.900.002 9.000.059.400.157.410.255.420.309.030.245.520.147.510.049.500.009 2.382.353.795.412.352.149.785.246 5.675.609.606.515.639.443.004.615.164.003.449.365.156.069.065.765 2.249.827.877.791.568.157.305.326 5.061.725.479.688.111.343.328.669.668.233.431.118.869.745.271.605 1.851.391.838.416.071.583.142.984 3.427.651.739.353.641.310.282.435.342.820.131.463.539.371.567.243 1.846.697.305.799.027.728.177.084 3.410.290.939.245.387.730.128.234.328.210.377.835.429.390.920.143 587.648.931.982.397.798.785.684 345.331.267.260.052.794.511.426.624.115.497.250.062.762.133.543 300.990.099.090.009.099.009.902 90.595.039.750.213.496.251.884.348.815.269.431.205.793.059.509 300.990.090.090.909.009.009.902 90.595.034.332.933.521.615.667.176.651.612.533.923.343.059.509 300.099.900.999.099.900.999.002 90.059.950.579.669.561.757.821.712.875.716.596.697.505.995.009 300.099.900.990.909.900.999.002 90.059.950.574.753.925.379.523.532.597.352.935.747.505.995.009 300.099.900.990.009.900.999.002 90.059.950.574.213.745.557.740.704.775.554.731.247.505.995.009 300.099.900.099.099.000.999.002 90.059.950.039.489.200.589.621.712.698.500.298.493.005.995.009 300.099.099.909.990.999.099.002 90.059.469.766.786.759.683.524.542.538.695.768.766.796.495.009 300.099.099.000.900.099.099.002 90.059.469.221.152.038.857.243.534.275.883.025.112.296.495.009 300.099.009.909.990.990.099.002 90.059.415.748.956.870.483.362.526.338.407.865.984.751.495.009 300.099.009.909.090.990.099.002 90.059.415.748.416.692.265.525.352.556.229.661.484.751.495.009 300.099.009.009.990.090.099.002 90.059.415.208.778.113.277.162.526.177.231.187.780.251.495.009 300.099.009.000.900.090.099.002 90.059.415.203.322.313.293.443.534.439.231.322.330.251.495.009 300.009.999.000.900.099.990.002 90.005.999.500.520.078.994.201.910.249.987.002.500.599.950.009 300.009.990.009.990.009.990.002 90.005.994.105.794.305.594.500.900.549.550.349.750.149.950.009 300.009.990.001.800.009.990.002 90.005.994.100.880.141.958.204.340.285.914.108.800.149.950.009 300.009.990.000.900.009.990.002 90.005.994.100.340.123.976.201.910.267.932.104.300.149.950.009 300.009.900.999.099.900.990.002 90.005.940.697.489.723.770.241.714.207.732.798.479.604.950.009 300.009.900.990.009.900.990.002 90.005.940.692.035.543.770.160.706.107.734.553.029.604.950.009 300.009.000.990.009.900.090.002 90.005.400.675.023.761.212.322.722.321.216.732.057.600.450.009 300.009.000.090.009.000.090.002 90.005.400.135.007.020.224.104.740.142.202.070.053.100.450.009 300.000.990.009.990.009.900.002 90.000.594.006.974.125.720.320.902.302.752.147.960.049.500.009 300.000.990.000.900.009.900.002 90.000.594.001.520.107.722.021.912.022.770.102.510.049.500.009 300.000.900.000.900.000.900.002 90.000.540.001.350.002.160.003.930.006.120.005.310.004.500.009 228.585.919.096.785.361.834.541 52.251.522.409.322.102.770.759.795.707.720.122.390.422.515.225 187.945.011.618.892.865.309.850 35.323.327.392.425.774.139.991.119.993.147.752.429.372.332.353 97.754.914.177.332.579.973.107 9.556.023.245.817.658.240.785.335.870.428.567.185.423.206.559 72.994.941.384.766.472.414.711 5.328.261.467.765.493.053.425.225.243.503.945.677.641.628.235 72.126.784.306.709.288.752.733 5.202.273.014.426.565.335.394.664.935.335.656.244.103.722.025 30.949.589.175.630.263.472.372 957.877.070.140.289.971.709.272.907.179.982.041.070.778.759 30.099.009.909.009.099.009.902 905.950.397.502.627.930.659.434.956.039.726.205.793.059.509 30.094.277.968.492.564.695.302 905.665.566.444.896.966.739.555.937.669.698.444.665.566.509 30.052.649.533.285.083.851.382 903.161.743.970.460.168.235.313.532.861.064.079.347.161.309 30.009.990.099.900.099.000.997 900.599.505.796.101.954.017.919.710.459.101.697.505.995.009 30.009.990.099.009.900.999.002 900.599.505.742.672.287.565.070.565.782.276.247.505.995.009 30.009.990.009.900.999.000.997 900.599.500.394.357.762.117.919.711.267.753.493.005.995.009 30.009.990.009.009.000.999.002 900.599.500.340.820.059.861.272.168.950.028.043.005.995.009 30.009.909.900.990.099.099.002 900.594.692.265.543.579.507.252.705.975.345.562.296.495.009 30.009.900.990.909.009.900.997 900.594.157.484.161.574.356.555.653.475.161.484.751.495.009 30.009.900.990.099.009.900.997 900.594.157.435.545.534.751.939.157.435.545.534.751.495.009 30.009.900.099.009.900.099.002 900.594.103.952.554.411.765.070.567.114.455.259.301.495.009 30.009.900.090.099.099.900.997 900.594.103.417.729.964.355.737.553.469.927.714.301.495.009 30.009.009.000.909.990.990.997 900.540.621.216.696.855.678.353.876.558.696.612.126.045.009 30.000.999.900.990.099.990.002 900.059.995.059.207.989.403.090.304.989.702.950.599.950.009 30.000.999.099.900.090.009.997 900.059.946.992.206.010.959.717.959.010.602.299.649.950.009 30.000.999.009.999.009.990.002 900.059.941.597.961.577.522.090.225.775.169.795.149.950.009 30.000.999.000.990.009.990.002 900.059.941.057.403.577.441.090.144.775.304.750.149.950.009 30.000.990.099.900.099.009.997 900.059.406.974.303.752.775.919.577.257.303.479.604.950.009 30.000.990.009.900.999.009.997 900.059.401.574.179.544.675.919.576.445.971.475.104.950.009 30.000.990.000.990.000.990.002 900.059.401.039.502.019.603.090.306.910.205.930.104.950.009 30.000.900.099.009.900.090.002 900.054.006.750.772.233.023.272.320.332.277.057.600.450.009 30.000.900.090.000.900.090.002 900.054.006.210.216.015.120.474.021.510.612.012.600.450.009 30.000.099.000.990.009.900.002 900.005.940.069.201.790.023.090.320.097.102.960.049.500.009 30.000.090.000.990.000.900.002 900.005.400.067.500.232.201.292.102.232.005.760.004.500.009 17.788.105.396.821.095.046.385 316.416.693.608.415.767.267.151.762.767.514.806.396.614.613 17.475.123.748.007.910.457.875 305.379.950.008.190.039.964.555.469.930.091.800.059.973.503 3.009.909.909.090.909.909.902 9.059.557.660.843.649.558.291.928.559.463.480.667.559.509 3.009.909.909.000.909.909.902 9.059.557.660.301.865.774.663.664.775.681.030.667.559.509 3.009.909.900.909.009.909.902 9.059.557.611.590.085.854.853.584.585.800.951.167.559.509 3.006.010.168.205.571.584.382 9.036.097.131.355.288.769.853.589.678.825.531.317.906.309 3.000.999.099.000.990.999.002 9.005.995.592.204.759.775.227.225.779.574.022.955.995.009 3.000.999.000.999.000.999.002 9.005.995.003.997.001.999.009.009.991.007.993.005.995.009 3.000.990.099.909.990.099.002 9.005.941.579.757.772.356.417.146.532.777.579.751.495.009 3.000.990.099.819.990.099.002 9.005.941.579.217.594.138.441.448.314.957.129.751.495.009 3.000.990.099.000.990.099.002 9.005.941.574.301.972.355.607.065.532.791.034.751.495.009 3.000.990.009.909.900.099.002 9.005.941.039.579.022.294.417.144.922.209.759.301.495.009 3.000.990.009.000.900.099.002 9.005.941.034.123.222.457.227.227.542.223.214.301.495.009 3.000.900.990.999.099.009.002 9.005.406.757.779.374.511.445.441.154.739.777.576.045.009 3.000.900.990.090.099.009.002 9.005.406.752.323.736.510.635.360.156.373.232.576.045.009 3.000.900.900.090.009.009.002 9.005.406.212.161.026.232.255.522.326.201.612.126.045.009 3.000.900.090.090.090.009.002 9.005.401.350.702.710.332.255.522.330.172.070.531.045.009 3.000.099.990.999.099.990.002 9.000.599.955.992.799.841.029.201.489.972.995.599.950.009 3.000.099.900.999.009.990.002 9.000.599.415.974.269.543.209.023.459.624.795.149.950.009 3.000.099.900.090.009.990.002 9.000.599.410.520.087.924.019.104.297.800.250.149.950.009 3.000.099.000.999.000.990.002 9.000.594.015.795.203.743.209.023.473.025.975.104.950.009 3.000.099.000.180.000.990.002 9.000.594.010.881.041.580.243.420.851.401.880.104.950.009 3.000.099.000.090.000.990.002 9.000.594.010.341.023.760.219.120.673.201.430.104.950.009 3.000.009.999.819.999.900.002 9.000.059.999.019.995.800.045.400.085.999.109.999.500.009 3.000.009.000.090.000.900.002 9.000.054.000.621.007.020.039.300.207.001.260.004.500.009 2.375.578.106.375.977.215.853 5.643.371.339.492.873.720.814.180.273.782.949.331.733.465 2.360.575.773.314.734.247.376 5.572.317.981.560.455.607.679.767.065.540.651.897.132.755 1.923.599.756.208.458.048.829 3.700.236.022.085.239.239.772.779.329.325.802.206.320.073 1.741.168.540.460.336.028.699 3.031.667.886.288.776.822.212.122.286.778.826.887.661.303 953.298.840.362.417.450.357 908.778.679.036.329.870.174.471.078.923.630.976.877.809 301.427.718.106.492.371.317 90.858.669.242.887.028.952.625.982.078.824.296.685.809 300.990.099.090.900.990.097 90.595.039.750.750.397.025.552.079.305.705.793.059.509 Prime!    300.990.090.090.990.990.097 90.595.034.332.982.872.605.550.627.828.923.343.059.509 300.099.909.990.009.000.997 90.059.955.976.011.504.197.179.140.511.067.955.995.009 300.099.900.990.099.000.997 90.059.950.574.267.223.359.195.332.276.247.505.995.009 300.099.900.099.000.999.002 90.059.950.039.430.379.810.901.897.303.493.005.995.009 300.099.099.900.999.099.002 90.059.469.761.389.837.432.723.473.898.316.796.495.009 300.099.099.009.900.900.997 90.059.469.226.554.303.937.373.930.345.562.296.495.009 300.099.009.900.990.099.002 90.059.415.743.554.553.470.707.435.545.534.751.495.009 300.099.000.990.099.900.997 90.059.410.395.255.981.359.195.318.955.259.301.495.009 300.090.099.009.900.990.997 90.054.067.523.772.179.737.373.797.127.732.576.045.009 300.090.009.009.909.990.997 90.054.013.507.567.859.575.357.595.876.570.531.045.009 300.009.900.999.900.990.002 90.005.940.697.970.393.040.904.039.307.979.604.950.009 300.009.900.909.099.009.997 90.005.940.643.487.406.985.358.960.478.434.604.950.009 300.009.900.099.000.990.002 90.005.940.157.412.554.230.903.245.521.475.104.950.009 300.009.000.990.099.909.997 90.005.400.675.077.768.777.177.786.777.057.600.450.009 240.280.211.058.694.930.483 57.734.579.826.410.981.565.856.518.901.462.897.543.775 189.944.266.461.823.324.539 36.078.824.361.720.141.015.951.014.102.716.342.887.063 181.513.572.458.558.855.479 32.947.176.986.668.495.870.907.859.486.668.967.174.923 178.710.345.804.265.977.810 31.937.387.697.480.326.379.397.362.308.479.678.373.913 72.327.492.042.616.761.241 5.231.266.105.174.790.917.337.190.974.715.016.621.325 30.099.009.099.909.009.902 905.950.348.796.405.386.454.683.504.697.843.059.509 30.009.990.099.900.999.002 900.599.505.796.155.972.090.279.551.697.505.995.009 30.009.990.009.000.999.002 900.599.500.340.339.780.191.087.933.043.005.995.009 30.009.909.990.999.099.002 900.594.697.667.867.542.373.245.768.766.796.495.009 30.009.909.981.999.099.002 900.594.697.127.689.162.616.261.986.721.796.495.009 30.009.900.990.990.099.002 900.594.157.489.028.526.171.625.820.984.751.495.009 30.009.900.909.090.099.002 900.594.152.573.406.750.555.057.604.375.251.495.009 30.009.900.900.090.099.002 900.594.152.033.228.534.272.435.822.330.251.495.009 30.000.990.099.900.990.002 900.059.406.974.357.214.090.412.753.479.604.950.009 30.000.990.009.000.990.002 900.059.401.520.177.222.191.222.771.025.104.950.009 30.000.900.009.000.090.002 900.054.001.350.021.600.393.006.120.053.100.450.009 24.074.611.755.709.552.708 579.586.931.188.148.591.979.195.841.881.139.685.975 18.067.816.535.853.143.779 326.445.994.373.248.296.797.692.842.373.499.544.623 17.642.418.543.871.212.010 311.254.932.077.130.816.707.618.031.770.239.452.113 6.295.866.490.138.952.534 39.637.934.861.654.573.311.337.545.616.843.973.693 3.009.909.909.909.909.902 9.059.557.665.773.881.945.491.883.775.667.559.509 3.009.900.990.900.990.097 9.059.503.975.026.762.073.702.676.205.793.059.509 3.009.900.909.909.009.902 9.059.503.487.471.085.745.475.801.747.843.059.509 3.000.999.009.900.999.002 9.005.995.057.426.776.309.036.776.247.505.995.009 3.000.990.990.099.099.002 9.005.946.922.655.970.527.250.795.562.296.495.009 3.000.990.099.009.900.997 9.005.941.574.355.455.391.935.545.534.751.495.009 3.000.990.090.909.900.997 9.005.941.525.739.415.853.585.149.375.251.495.009 3.000.990.009.900.099.002 9.005.941.039.520.196.309.036.910.259.301.495.009 3.000.900.990.099.009.002 9.005.406.752.377.212.527.252.127.732.576.045.009 3.000.900.090.090.009.002 9.005.401.350.702.224.147.414.222.070.531.045.009 3.000.099.009.900.990.002 9.000.594.069.208.900.509.050.098.029.604.950.009 3.000.090.009.900.090.002 9.000.540.067.502.322.129.212.232.057.600.450.009 1.987.476.933.990.142.634 3.950.064.563.142.857.782.877.582.413.654.600.593 1.770.410.114.442.237.085 Prime!    3.134.351.973.319.375.014.105.739.133.791.534.313 300.990.990.909.909.902 90.595.576.608.929.465.556.492.980.667.559.509 300.900.909.090.900.902 90.541.357.091.730.609.390.603.719.075.314.509 300.099.900.900.999.002 90.059.950.520.789.421.912.498.702.505.995.009 300.099.009.990.099.002 90.059.415.797.037.540.904.573.079.751.495.009 300.099.001.800.099.002 90.059.410.881.415.824.342.851.418.801.495.009 300.099.000.900.099.002 90.059.410.341.237.621.912.673.214.301.495.009 300.090.099.099.009.002 90.054.067.577.253.043.734.035.277.576.045.009 300.090.090.009.009.002 90.054.062.121.615.124.742.151.612.126.045.009 300.009.998.199.990.002 90.005.999.019.958.004.540.085.991.099.950.009 300.009.000.900.090.002 90.005.400.621.070.203.930.207.012.600.450.009 30.099.099.090.090.097 905.955.766.035.062.535.260.530.667.559.509 30.099.090.099.090.097 905.955.224.793.143.535.341.397.422.559.509 30.099.009.090.990.097 905.950.348.259.504.535.405.952.843.059.509 30.099.009.009.009.902 905.950.343.324.459.272.954.423.343.059.509 Prime!    30.090.090.909.099.097 905.413.570.917.848.151.848.719.075.314.509 30.009.990.990.999.002 900.599.559.279.841.292.148.972.955.995.009 30.009.909.900.900.997 900.594.692.260.195.717.591.062.296.495.009 30.009.900.990.099.002 900.594.157.435.545.090.545.534.751.495.009 Prime!    30.009.009.900.990.997 900.540.675.237.775.717.577.732.576.045.009 22.797.812.361.579.671 519.740.248.473.794.878.497.374.842.047.915 22.683.451.840.157.828 514.538.987.384.759.575.957.483.789.835.415 19.007.389.738.417.935 361.280.864.668.115.434.511.866.468.082.163 17.587.931.732.323.900 309.335.342.620.885.999.588.026.243.533.903 3.009.909.909.909.902 9.059.557.665.773.837.383.775.667.559.509 3.009.900.909.009.902 9.059.503.482.058.637.368.502.843.059.509 3.009.090.090.090.902 9.054.623.170.283.275.723.820.713.264.509 3.009.009.090.900.902 9.054.135.709.124.275.724.219.075.314.509 3.000.990.999.099.002 9.005.946.976.673.229.223.766.796.495.009 3.000.990.090.099.002 9.005.941.520.872.419.142.780.251.495.009 3.000.900.090.009.002 9.005.401.350.216.039.306.120.531.045.009 2.434.467.459.876.868 5.926.631.813.199.332.339.913.181.366.295 2.328.650.332.630.593 5.422.612.371.660.573.750.661.732.162.245 1.746.916.031.844.124 3.051.715.622.314.022.204.132.265.171.503 300.990.990.090.097 90.595.576.115.417.171.451.167.559.509 300.990.099.009.902 90.595.039.701.990.909.910.793.059.509 300.990.090.990.097 90.595.034.874.227.172.247.843.059.509 300.900.909.099.097 Prime!    90.541.357.096.663.336.669.075.314.509 300.090.099.009.002 90.054.067.523.232.923.232.576.045.009 229.001.028.816.941 52.441.471.199.217.671.299.117.414.425 198.267.378.873.165 39.309.953.525.235.353.252.535.990.393 196.911.378.423.380 38.774.090.952.595.759.525.909.047.783 185.315.401.886.740 34.341.798.176.444.144.467.189.714.343 175.962.987.683.099 30.962.973.034.362.626.343.037.926.903 30.099.009.009.902 905.950.343.378.191.873.343.059.509 30.090.990.990.902 905.467.738.814.575.418.837.764.509 30.090.090.900.902 905.413.570.424.575.424.075.314.509 30.009.981.999.002 900.599.019.580.454.085.910.995.009 30.009.009.009.002 900.540.621.702.393.207.126.045.009 19.017.332.697.439 361.658.942.925.101.529.249.856.163 18.349.377.330.605 336.699.648.420.939.024.846.996.633 17.601.866.803.275 309.825.714.960.252.069.417.528.903 7.095.660.661.226 50.348.400.219.277.291.200.484.305 3.086.915.322.647 9.529.046.209.195.919.026.409.259 3.085.682.084.872 9.521.433.928.903.098.293.341.259 3.009.909.909.902 9.059.557.665.729.275.667.559.509 3.009.909.090.097 9.059.552.730.651.560.372.559.509 3.009.090.090.902 9.054.623.175.167.615.713.264.509 3.009.009.099.097 9.054.135.758.451.548.575.314.509 1.953.167.924.219 3.814.864.940.199.910.494.684.183 1.897.132.914.325 3.599.113.294.617.164.923.119.953 1.755.185.230.175 3.080.675.192.226.222.915.760.803 300.990.909.902 90.595.527.843.934.872.559.509 300.900.900.902 90.541.352.163.936.125.314.509 181.723.112.005 33.023.289.436.963.498.232.033 71.171.663.326 5.065.405.660.660.665.045.605 57.747.550.569 3.334.779.596.776.959.774.333 30.090.990.902 905.467.733.494.337.764.509 22.486.248.626 505.631.377.292.773.136.505 19.707.956.144 388.403.535.393.535.304.883 3.009.819.902 9.059.015.845.485.109.509 3.009.090.902 9.054.628.059.508.264.509 2.411.508.138 5.815.371.502.051.735.185 2.381.776.121 5.672.857.492.947.582.765 2.315.681.863 5.362.382.492.942.832.635 727.913.433 529.857.966.669.758.925 726.714.741 528.114.315.513.411.825 589.167.859 347.118.766.667.811.743 549.199.524 301.620.117.711.026.103 Prime!    309.230.287 95.623.370.707.332.659 230.098.566 52.945.350.305.354.925 177.865.385 31.636.095.359.063.613 76.675.186 5.879.084.224.809.785 62.127.180 3.859.786.556.879.583 30.909.092 955.371.999.173.559 18.886.025 356.681.959.186.653 17.605.724 309.961.535.169.903 5.492.899 30.171.944.917.103 3.093.852 9.571.923.291.759 598.350 358.023.320.853 237.721 56.511.511.565 Prime!    230.663 53.205.650.235 75.146 5.646.996.465 73.188 5.356.556.535 30.947 957.747.759 23.111 534.141.435 6.154 37.877.873 2.431 5.912.195 753 567.765 243 59.295 184 34.043 Prime!    179 32.223 175 Prime!    30.803 Prime!    71 5.115 60 3.663 Prime!    23 555 Prime!    19 Prime!    383 Prime!    5 33 Prime!    2 9 1 Prime!    5 0 Prime!    3
 [QM4] Case X = 4 One can find the regular numbers of the form n2+(n+4) at %N n^2 + (n+4). under A027689. The palindromic numbers of the form n2+(n+4) are categorised as follows : %N n^2 + (n+4) is a palindrome. under A027716. %N Palindromes of the form n^2 + (n+4). under A027717. More terms from Giovanni Resta, Aug 29, 2018. See Index Nrs 33 up to 36. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 37 up to 57. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 58 up to 70. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 71 up to 77. More terms from Patrick De Geest, Jun 22, 2023. See Index Nrs 78 up to 81. More terms from Patrick De Geest, Jul 18, 2023. See Index Nr 82. 2.000.000.000.000.000.000.000.000.000 4.000.000.000.000.000.000.000.000.002.000.000.000.000.000.000.000.000.004 263.599.064.210.346.216.030.151.843 69.484.466.652.570.227.367.225.174.047.152.276.372.207.525.666.448.496 259.161.643.409.192.300.142.862.316 67.164.757.414.553.346.783.385.003.830.058.338.764.335.541.475.746.176 209.723.971.282.573.306.843.931.969 43.984.144.130.533.633.099.669.453.535.496.699.033.633.503.144.148.934 200.000.000.000.000.000.000.000.000 40.000.000.000.000.000.000.000.000.200.000.000.000.000.000.000.000.004 20.000.000.000.000.000.000.000.000 400.000.000.000.000.000.000.000.020.000.000.000.000.000.000.000.004 2.216.679.932.356.152.498.755.090 4.913.669.922.510.476.817.570.972.790.757.186.740.152.299.663.194 2.000.000.000.000.000.000.000.000 4.000.000.000.000.000.000.000.002.000.000.000.000.000.000.000.004 213.889.222.221.047.345.477.749 45.748.599.382.324.573.547.664.046.674.537.542.328.399.584.754 200.000.000.000.000.000.000.000 40.000.000.000.000.000.000.000.200.000.000.000.000.000.000.004 25.392.831.461.173.895.119.806 644.795.889.615.582.773.459.303.954.377.285.516.988.597.446 20.000.000.000.000.000.000.000 400.000.000.000.000.000.000.020.000.000.000.000.000.000.004 2.520.666.561.707.904.605.811 6.353.759.915.312.349.657.994.997.569.432.135.199.573.536 2.000.000.000.000.000.000.000 4.000.000.000.000.000.000.002.000.000.000.000.000.000.004 245.706.621.055.561.922.226 60.371.743.630.541.505.336.163.350.514.503.634.717.306 212.324.863.448.228.312.574 45.081.847.638.308.799.321.112.399.780.383.674.818.054 211.254.379.519.623.010.415 44.628.412.866.220.914.028.882.041.902.266.821.482.644 208.827.701.545.597.915.394 43.609.008.932.817.317.982.128.971.371.823.980.090.634 200.000.000.000.000.000.000 40.000.000.000.000.000.000.200.000.000.000.000.000.004 25.093.514.750.456.275.558 629.684.482.531.366.677.414.776.663.135.284.486.926 24.779.742.894.344.292.828 614.035.657.909.806.470.777.074.608.909.756.530.416 24.758.349.323.692.745.603 612.975.861.233.997.033.616.330.799.332.168.579.216 22.326.360.372.535.840.790 498.466.367.484.338.727.565.727.833.484.763.664.894 20.019.380.272.243.422.999 400.775.586.484.689.149.171.941.986.484.685.577.004 20.000.000.000.000.000.000 400.000.000.000.000.000.020.000.000.000.000.000.004 2.456.920.322.636.915.226 6.036.457.471.786.283.611.163.826.871.747.546.306 2.019.265.573.385.942.299 4.077.433.455.861.658.326.238.561.685.543.347.704 2.000.000.000.000.000.000 4.000.000.000.000.000.002.000.000.000.000.000.004 251.777.501.269.233.963 63.391.910.145.379.110.101.197.354.101.919.336 200.000.000.000.000.000 40.000.000.000.000.000.200.000.000.000.000.004 21.502.431.241.622.339 462.354.549.300.696.424.696.003.945.453.264 20.000.000.000.000.000 400.000.000.000.000.020.000.000.000.000.004 2.464.706.598.254.901 6.074.778.615.481.248.421.845.168.774.706 2.209.415.043.638.519 4.881.514.835.056.201.026.505.384.151.884 2.103.611.085.905.640 4.425.179.600.745.108.015.470.069.715.244 2.000.000.000.000.000 4.000.000.000.000.002.000.000.000.000.004 260.565.021.991.216 67.894.130.685.283.138.258.603.149.876 220.867.190.255.619 48.782.315.731.412.021.413.751.328.784 210.855.962.500.840 44.460.236.922.155.855.122.963.206.444 200.000.000.000.000 40.000.000.000.000.200.000.000.000.004 25.142.773.284.288 632.159.048.425.131.524.840.951.236 25.075.537.810.133 628.782.596.467.434.764.695.287.826 24.884.321.704.671 619.229.466.701.585.107.664.922.916 20.217.027.652.824 408.728.207.115.070.511.702.827.804 20.139.827.049.124 405.612.633.568.646.865.336.216.504 20.000.000.000.000 400.000.000.000.020.000.000.000.004 2.537.387.874.018 6.438.337.223.216.123.227.338.346 2.451.351.151.126 6.009.122.466.129.216.642.219.006 2.007.806.131.300 4.031.285.460.887.880.645.821.304 2.000.000.000.000 4.000.000.000.002.000.000.000.004 200.000.000.000 40.000.000.000.200.000.000.004 24.784.431.171 614.268.028.494.820.862.416 21.572.321.960 465.365.074.767.470.563.564 20.349.812.814 414.114.881.585.188.411.414 20.102.030.400 404.091.626.222.626.190.404 20.000.000.000 400.000.000.020.000.000.004 2.094.600.194 4.387.349.974.799.437.834 2.000.000.000 4.000.000.002.000.000.004 205.705.704 42.314.836.863.841.324 200.000.000 40.000.000.200.000.004 25.882.353 669.896.222.698.966 20.000.000 400.000.020.000.004 2.620.486 6.866.949.496.686 2.490.266 6.201.427.241.026 2.155.139 4.644.626.264.464 2.000.000 4.000.002.000.004 218.354 47.678.687.674 205.704 42.314.341.324 202.885 41.162.526.114 200.000 40.000.200.004 20.604 424.545.424 20.000 400.020.004 2.613 6.830.386 Prime!    2.551 6.510.156 2.234 4.992.994 2.000 4.002.004 261 68.386 219 48.184 200 40.204 20 424 1 6 0 4 [QM5] Case X = 5 One can find the regular numbers of the form n2+(n+5) at %N n^2 + (n+5). under A027690. The palindromic numbers of the form n2+(n+5) are categorised as follows : %N n^2 + (n+5) is a palindrome. under A027718. %N Palindromes of the form n^2 + (n+5). under A027728. More terms from Giovanni Resta, Aug 28, 2018. See Index Nrs 30 up to 46. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 47 up to 79. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 80 up to 87. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 88 up to 94. More terms from Robert Xiao, Jul 18, 2023. See Index Nrs 95 up to 97. 2.741.097.489.407.795.894.534.146.448 7.513.615.446.437.721.726.230.412.801.082.140.326.271.277.346.445.163.157 2.321.583.477.758.376.828.874.021.805 5.389.749.844.200.679.760.082.306.490.946.032.800.679.760.024.489.479.835 2.312.974.744.804.653.668.859.324.594 5.349.852.170.104.152.764.124.581.678.761.854.214.672.514.010.712.589.435 7.724.893.520.176.131.722.830.409 59.673.979.898.059.188.008.749.155.194.780.088.195.089.897.937.695 7.168.715.561.822.749.647.862.085 51.390.482.806.319.661.128.549.322.394.582.116.691.360.828.409.315 276.930.549.956.726.857.275.578 76.690.529.499.335.189.572.067.476.027.598.153.399.492.509.667 231.039.377.440.567.687.892.430 53.379.193.928.125.097.468.095.059.086.479.052.182.939.197.335 34.440.033.402.705.514.519.042 1.186.115.900.779.471.580.807.337.080.851.749.770.095.116.811 23.148.775.498.877.278.516.494 535.865.807.097.420.994.859.868.958.499.024.790.708.568.535 10.657.437.381.077.853.690.857 113.580.971.531.595.580.831.393.138.085.595.135.179.085.311 8.773.059.802.826.288.434.478 76.966.578.303.966.434.903.444.430.943.466.930.387.566.967 2.817.140.814.595.263.786.456 7.936.282.369.258.466.412.199.912.146.648.529.632.826.397 2.701.333.536.188.917.348.558 7.297.202.873.738.920.834.422.244.380.298.373.782.027.927 1.094.835.918.541.132.095.737 1.198.665.688.527.804.433.884.883.344.087.258.865.668.911 1.049.185.679.191.036.040.877 1.100.790.589.419.555.597.559.557.955.559.149.850.970.011 233.630.688.688.326.669.315 54.583.298.696.981.811.115.651.111.818.969.689.238.545 128.666.957.189.116.742.292 16.555.185.872.306.000.532.823.500.060.327.858.155.561 12.655.405.880.861.430.032 Prime!    160.159.298.009.342.067.797.760.243.900.892.951.061 3.438.846.839.357.135.357 11.825.667.584.556.559.511.595.565.548.576.652.811 2.821.048.328.990.795.231 7.958.313.674.501.758.047.408.571.054.763.138.597 2.808.651.171.354.901.886 7.888.521.402.353.262.439.342.623.532.041.258.887 2.662.636.067.713.063.398 7.089.630.829.086.485.135.315.846.809.280.369.807 Prime!    1.266.537.051.930.343.607 1.604.116.103.912.405.899.985.042.193.016.114.061 1.092.269.214.303.220.062 1.193.052.036.514.573.674.763.754.156.302.503.911 1.065.112.309.613.110.542 1.134.464.232.089.374.652.564.739.802.324.644.311 854.071.216.890.041.433 729.437.643.520.036.195.591.630.025.346.734.927 710.487.567.770.103.224 504.792.583.955.877.022.220.778.559.385.297.405 272.740.912.616.759.106 74.387.605.415.022.626.762.622.051.450.678.347 128.516.445.113.554.267 16.516.476.664.625.206.560.252.646.667.461.561 127.555.335.548.680.952 16.270.363.626.936.590.709.563.962.636.307.261 127.325.246.849.329.752 16.211.718.485.242.756.065.724.258.481.711.261 73.856.398.697.590.940 5.454.767.628.577.512.772.157.758.267.674.545 28.182.867.034.430.531 794.273.994.280.391.181.193.082.499.372.497 24.124.980.160.964.119 582.014.667.766.912.353.219.667.766.410.285 10.891.052.175.305.917 118.615.017.485.235.757.532.584.710.516.811 10.742.267.540.559.297 115.396.311.912.953.898.359.219.113.693.511 7.649.794.162.480.819 58.519.350.728.325.622.652.382.705.391.585 7.200.217.655.047.414 51.843.134.280.056.488.465.008.243.134.815 Prime!    2.709.031.479.580.963 7.338.851.557.360.624.260.637.551.588.337 2.689.612.932.909.633 7.234.017.728.874.760.674.788.277.104.327 2.391.927.132.618.754 5.721.315.407.757.776.777.577.045.131.275 1.274.252.737.050.152 1.623.720.037.879.805.089.787.300.273.261 709.962.501.910.224 504.046.754.118.625.526.811.457.640.405 266.915.367.273.771 71.243.813.286.892.329.868.231.834.217 264.586.807.048.126 70.006.178.463.922.522.936.487.160.007 128.523.687.718.107 16.518.338.304.661.616.640.383.381.561 127.307.298.113.552 16.207.148.152.972.927.925.184.170.261 107.441.307.275.097 11.543.634.508.981.918.980.543.634.511 106.650.062.701.657 11.374.235.874.267.476.247.853.247.311 104.926.659.615.122 Prime!    11.009.603.897.987.778.979.830.690.011 10.685.559.255.237 114.181.176.597.191.795.671.181.411 2.724.617.501.718 7.423.540.530.670.760.350.453.247 2.413.553.760.255 5.825.241.753.643.463.571.425.285 1.274.687.352.352 1.624.827.846.247.426.487.284.261 1.092.675.882.737 1.193.940.584.716.174.850.493.911 712.311.093.700 507.387.094.208.802.490.783.705 128.760.203.492 16.579.190.003.430.009.197.561 127.651.865.352 16.294.998.727.972.789.949.261 87.304.087.378 7.622.003.672.992.763.002.267 84.526.784.828 7.144.777.353.443.537.774.417 27.413.239.448 751.485.697.060.796.584.157 24.070.821.945 579.404.469.131.964.404.975 23.203.983.194 538.424.836.090.638.424.835 4.029.203.527 16.234.481.066.018.443.261 2.815.069.131 7.924.614.215.124.164.297 2.781.875.716 Prime!    7.738.832.502.052.388.377 2.765.569.146 7.648.372.704.072.738.467 2.426.472.519 5.887.768.887.888.677.885 2.237.334.999 5.005.667.899.987.665.005 Prime!    106.617.617 11.367.316.361.376.311 87.579.753 7.670.213.223.120.767 85.125.933 7.246.424.554.246.427 7.569.245 57.293.477.439.275 4.063.892 16.515.222.251.561 2.775.383 7.702.753.572.077 2.724.718 Prime!    7.424.090.904.247 2.358.150 5.560.873.780.655 107.422 11.539.593.511 105.322 11.092.829.011 28.168 793.464.397 27.548 758.919.857 22.424 502.858.205 12.752 162.626.261 4.067 16.544.561 4.012 16.100.161 3.462 11.988.911 2.751 7.570.757 230 53.135 224 50.405 Prime!    127 16.261 74 5.555 26 707 12 161 8 77 Prime!    2 Prime!    11 1 Prime!    7 0 Prime!    5 [QM6] Case X = 6 One can find the regular numbers of the form n2+(n+6) at %N n^2 + (n+6). under A027691. The palindromic numbers of the form n2+(n+6) are categorised as follows : %N n^2 + (n+6) is a palindrome. under A027729. %N Palindromes of the form n^2 + (n+6). under A027721. More terms from Giovanni Resta, Aug 27, 2018. See Index Nrs 32 up to 34. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 35 up to 54. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 55 up to 63. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 64 up to 75. More terms from Patrick De Geest, Jun 22, 2023. See Index Nrs 76 up to 78. More terms from Patrick De Geest, Jul 18, 2023. See Index Nr 79. 2.874.297.145.398.462.335.096.954.658 8.261.584.080.045.749.329.477.192.378.732.917.749.239.475.400.804.851.628 283.829.342.698.845.400.785.348.373 80.559.095.776.858.625.017.648.318.381.384.671.052.685.867.759.095.508 Prime!    147.801.308.817.066.431.064.004.717 21.845.226.888.037.839.135.901.010.701.010.953.193.873.088.862.254.812 146.510.768.911.536.844.179.295.762 21.465.405.407.049.751.032.909.322.022.390.923.015.794.070.450.456.412 28.808.030.648.133.248.701.533.566 829.902.629.823.784.565.259.188.131.881.952.565.487.328.926.209.928 25.498.075.419.925.390.458.470.425 650.151.850.120.203.376.966.060.141.060.669.673.302.021.058.151.056 25.244.234.944.717.175.068.503.830 637.271.397.944.079.754.987.094.323.490.789.457.970.449.793.172.736 14.783.442.152.732.972.665.836.442 218.550.161.883.202.109.113.317.797.713.311.901.202.388.161.055.812 2.615.815.820.738.709.802.614.544 6.842.492.408.026.929.976.682.097.902.866.799.296.208.042.942.486 2.570.320.002.048.220.603.364.460 6.606.544.912.929.164.766.674.687.864.766.674.619.292.194.456.066 1.469.399.355.246.223.578.086.222 2.159.134.465.198.017.558.712.001.002.178.557.108.915.644.319.512 1.460.737.055.811.722.509.118.057 2.133.752.746.221.499.320.551.537.351.550.239.941.226.472.573.312 292.438.232.461.254.812.293.351 85.520.119.805.062.907.829.875.157.892.870.926.050.891.102.558 260.165.118.520.509.050.834.229 67.685.888.894.790.521.531.640.304.613.512.509.749.888.858.676 147.893.672.859.830.109.963.482 21.872.538.471.970.449.256.634.243.665.294.407.917.483.527.812 28.985.874.843.495.529.237.006 840.180.940.442.786.971.539.080.935.179.687.244.049.081.048 2.987.335.598.947.757.919.131 8.924.173.980.740.559.545.114.115.459.550.470.893.714.298 1.615.639.009.407.151.056.787 2.610.289.408.718.120.340.968.690.430.218.178.049.820.162 296.053.623.414.021.923.183 87.647.747.936.571.509.891.219.890.517.563.974.774.678 293.185.592.806.891.151.151 85.957.791.829.528.184.310.901.348.182.592.819.775.958 286.353.194.167.746.026.328 81.998.151.810.070.856.868.086.865.807.001.815.189.918 259.892.958.171.568.404.329 67.544.349.707.168.604.230.503.240.686.170.794.344.576 254.235.549.230.472.251.415 64.635.714.492.519.879.788.888.797.891.529.441.753.646 163.435.381.459.705.732.227 26.711.123.912.879.524.200.300.242.597.821.932.111.762 14.794.168.948.789.166.882 218.867.434.885.317.563.080.365.713.588.434.768.812 2.985.831.125.619.083.431 8.915.187.510.715.722.782.872.275.170.157.815.198 2.916.855.303.079.661.851 8.508.044.859.103.945.996.995.493.019.584.408.058 2.551.552.617.878.235.474 6.510.420.761.801.276.736.376.721.081.670.240.156 1.463.508.671.957.677.637 2.141.857.632.895.325.294.925.235.982.367.581.412 254.045.687.862.089.940 64.539.211.521.322.432.123.422.312.511.293.546 162.090.760.203.886.327 26.273.414.543.473.779.597.737.434.541.437.262 147.870.657.622.296.957 21.865.731.385.650.569.296.505.658.313.756.812 29.498.083.994.743.008 870.136.959.360.913.646.319.063.959.631.078 14.500.619.401.279.597 210.267.963.020.766.272.667.020.369.762.012 287.460.767.600.658 82.633.692.909.559.795.590.929.633.628 255.814.556.383.825 65.441.087.257.853.435.875.278.014.456 162.126.124.865.152 26.284.880.363.791.019.736.308.848.262 26.199.714.854.344 686.425.058.448.959.844.850.524.686 2.610.993.061.219 6.817.284.765.736.375.674.827.186 2.565.389.200.649 6.581.221.750.809.080.571.221.856 2.497.478.799.079 6.237.400.351.851.581.530.047.326 1.630.700.084.692 2.659.182.766.216.126.672.819.562 1.614.498.398.967 2.606.605.080.268.620.805.066.062 293.212.995.776 85.973.860.892.229.806.837.958 286.306.469.671 81.971.394.575.757.549.317.918 29.959.390.368 897.565.071.252.170.565.798 28.988.127.118 840.311.513.838.315.113.048 2.931.604.151 8.594.302.901.092.034.958 2.853.889.203 8.144.683.585.853.864.418 288.888.888 83.456.789.898.765.438 264.056.434 69.725.800.600.852.796 148.278.137 21.986.406.060.468.912 29.585.508 875.302.313.203.578 29.190.748 852.099.797.990.258 28.888.888 834.567.878.765.438 16.353.547 267.438.515.834.762 14.604.657 213.296.020.692.312 2.995.631 8.973.808.083.798 Prime!    2.985.943 8.915.858.585.198 2.960.816 8.766.434.346.678 2.952.316 8.716.172.716.178 2.888.888 8.345.676.765.438 2.873.233 8.255.470.745.528 Prime!    2.834.101 8.032.131.312.308 292.276 85.425.552.458 288.888 83.456.565.438 264.334 69.872.727.896 Prime!    146.777 21.543.634.512 28.888 834.545.438 2.946 8.681.868 2.888 8.343.438 2.550 6.505.056 2.485 6.177.716 288 83.238 28 818 25 656 24 606 1 8 0 6 [QM7] Case X = 7 One can find the regular numbers of the form n2+(n+7) at %N n^2 + (n+7). under A027692. The palindromic numbers of the form n2+(n+7) are categorised as follows : %N n^2 + (n+7) is a palindrome. under A027722. %N Palindromes of the form n^2 + (n+7). under A027723. More terms from Giovanni Resta, Aug 28, 2018. See Index Nrs 28 up to 45. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 46 up to 71. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 72 up to 80. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 81 up to 96. More terms from Patrick De Geest, Jun 22, 2023. See Index Nrs 97 up to 99. More terms from Patrick De Geest, Jul 18, 2023. See Index Nrs 100 up to 103. 3.121.000.000.000.000.000.000.001.208 9.740.641.000.000.000.000.000.007.543.457.000.000.000.000.000.001.460.479 3.000.000.000.000.000.000.000.000.001 9.000.000.000.000.000.000.000.000.009.000.000.000.000.000.000.000.000.009 2.821.774.784.748.357.549.523.525.409 7.962.412.935.841.639.581.883.069.452.549.603.881.859.361.485.392.142.697 2.772.985.384.440.605.266.228.026.635 7.689.447.942.321.211.382.921.626.343.436.261.292.831.121.232.497.449.867 315.379.187.639.614.006.145.294.156 99.464.031.996.222.859.912.937.826.762.873.921.995.822.269.913.046.499 312.100.000.000.000.000.000.001.208 97.406.410.000.000.000.000.000.754.345.700.000.000.000.000.001.460.479 300.000.000.000.000.000.000.000.001 90.000.000.000.000.000.000.000.000.900.000.000.000.000.000.000.000.009 31.210.000.000.000.000.000.001.208 974.064.100.000.000.000.000.075.434.570.000.000.000.000.001.460.479 30.000.000.000.000.000.000.000.001 900.000.000.000.000.000.000.000.090.000.000.000.000.000.000.000.009 3.121.000.000.000.000.000.001.208 9.740.641.000.000.000.000.007.543.457.000.000.000.000.001.460.479 3.100.357.559.888.528.326.840.046 9.612.216.999.157.949.510.797.804.087.970.159.497.519.996.122.169 3.082.675.293.024.238.368.864.523 9.502.886.962.222.073.890.683.161.613.860.983.702.222.696.882.059 3.000.000.000.000.000.000.000.001 9.000.000.000.000.000.000.000.009.000.000.000.000.000.000.000.009 2.654.409.154.426.579.861.084.775 7.045.887.959.103.630.692.532.923.292.352.960.363.019.597.885.407 1.916.823.575.746.489.052.351.172 3.674.212.620.537.556.253.609.519.159.063.526.557.350.262.124.763 312.100.000.000.000.000.001.208 97.406.410.000.000.000.000.754.345.700.000.000.000.001.460.479 300.000.000.000.000.000.000.001 90.000.000.000.000.000.000.000.900.000.000.000.000.000.000.009 177.682.217.094.375.865.696.622 31.570.970.271.572.915.105.447.074.450.151.927.517.207.907.513 176.938.468.365.190.722.850.142 31.307.221.587.419.598.191.197.879.119.189.591.478.512.270.313 31.210.000.000.000.000.001.208 974.064.100.000.000.000.075.434.570.000.000.000.001.460.479 30.616.010.059.832.974.528.836 937.340.071.983.793.896.589.191.985.698.397.389.170.043.739 30.000.000.000.000.000.000.001 900.000.000.000.000.000.000.090.000.000.000.000.000.000.009 27.680.644.579.504.590.686.564 766.218.084.336.856.878.146.585.641.878.658.633.480.812.667 3.121.000.000.000.000.001.208 9.740.641.000.000.000.007.543.457.000.000.000.001.460.479 3.000.000.000.000.000.000.001 9.000.000.000.000.000.000.009.000.000.000.000.000.000.009 312.100.000.000.000.001.208 97.406.410.000.000.000.754.345.700.000.000.001.460.479 300.000.000.000.000.000.001 90.000.000.000.000.000.000.900.000.000.000.000.000.009 31.506.730.336.917.391.243 992.674.056.523.230.669.939.966.032.325.650.476.299 31.210.000.000.000.001.208 974.064.100.000.000.075.434.570.000.000.001.460.479 31.195.432.792.677.686.716 973.155.027.122.470.376.101.673.074.221.720.551.379 30.000.000.000.000.000.001 900.000.000.000.000.000.090.000.000.000.000.000.009 27.622.856.194.472.462.135 763.022.184.340.505.672.888.276.505.043.481.220.367 3.121.000.000.000.001.208 9.740.641.000.000.007.543.457.000.000.001.460.479 3.021.993.199.130.681.096 9.132.442.895.592.088.370.738.802.955.982.442.319 3.000.000.000.000.000.001 9.000.000.000.000.000.009.000.000.000.000.000.009 2.722.509.353.145.589.459 7.412.057.177.965.215.939.395.125.697.717.502.147 1.915.035.496.742.374.887 3.667.360.953.783.314.538.354.133.873.590.637.663 312.100.000.000.001.208 97.406.410.000.000.754.345.700.000.001.460.479 300.000.000.000.000.001 90.000.000.000.000.000.900.000.000.000.000.009 277.182.107.823.074.739 76.829.920.897.242.630.703.624.279.802.992.867 191.130.616.729.367.092 36.530.912.651.348.219.891.284.315.621.903.563 31.210.000.000.001.208 974.064.100.000.075.434.570.000.001.460.479 30.648.097.516.689.388 939.305.881.392.502.262.205.293.188.503.939 30.000.000.000.000.001 900.000.000.000.000.090.000.000.000.000.009 19.124.750.677.376.132 365.756.088.471.798.838.897.174.880.657.563 3.137.955.834.553.086 9.846.766.819.605.757.575.069.186.676.489 3.121.000.000.001.208 9.740.641.000.007.543.457.000.001.460.479 3.083.258.898.592.148 9.506.485.435.747.668.667.475.345.846.059 3.000.000.000.000.001 9.000.000.000.000.009.000.000.000.000.009 2.702.530.723.613.869 7.303.672.312.076.905.096.702.132.763.037 312.100.000.001.208 97.406.410.000.754.345.700.001.460.479 300.000.000.000.001 90.000.000.000.000.900.000.000.000.009 268.792.508.783.804 72.249.412.778.291.619.287.721.494.227 264.773.198.830.100 70.104.846.818.723.932.781.864.840.107 177.377.074.711.837 31.462.626.633.328.782.333.662.626.413 31.210.000.001.208 974.064.100.075.434.570.001.460.479 30.000.000.000.001 900.000.000.000.090.000.000.000.009 17.615.399.751.397 310.302.308.401.535.104.803.203.013 3.149.974.520.756 9.922.339.481.415.141.849.332.299 3.121.000.001.208 9.740.641.007.543.457.001.460.479 3.041.875.952.766 9.253.009.312.019.102.139.003.529 3.000.000.000.001 9.000.000.000.009.000.000.000.009 2.702.976.653.994 7.306.082.792.039.302.972.806.037 1.900.006.888.012 3.610.026.174.494.944.716.200.163 312.100.001.208 97.406.410.754.345.701.460.479 300.000.000.001 90.000.000.000.900.000.000.009 281.757.625.709 79.387.359.645.454.695.378.397 275.313.182.749 75.797.348.595.659.584.379.757 266.584.070.214 71.067.066.492.129.466.076.017 31.210.001.208 974.064.175.434.571.460.479 31.006.644.078 Prime!    961.411.977.010.779.114.169 30.805.056.481 948.951.504.828.405.159.849 Prime!    30.000.000.001 900.000.000.090.000.000.009 28.255.878.334 798.394.660.454.066.493.897 26.928.832.879 725.162.040.252.040.261.527 3.121.001.208 9.740.648.543.458.460.479 3.000.000.001 9.000.000.009.000.000.009 2.817.818.390 7.940.100.481.840.010.497 2.673.533.185 7.147.779.693.969.777.417 303.758.458 92.269.201.110.296.229 300.000.001 90.000.000.900.000.009 30.122.098 907.340.818.043.709 Prime!    30.000.001 900.000.090.000.009 27.515.125 757.082.131.280.757 3.000.001 9.000.009.000.009 1.762.122 3.105.075.705.013 312.208 97.474.147.479 300.001 90.000.900.009 177.237 31.413.131.413 30.001 900.090.009 Prime!    27.259 743.080.347 Prime!    3.001 9.009.009 2.764 7.642.467 Prime!    1.777 3.159.513 Prime!    313 98.289 301 90.909 280 78.687 274 75.357 177 Prime!    31.513 Prime!    31 999 Prime!    17 Prime!    313 1 9 0 Prime!    7 [QM8] Case X = 8 One can find the regular numbers of the form n2+(n+8) at %N n^2 + (n+8). under A027693. The palindromic numbers of the form n2+(n+8) are categorised as follows : %N n^2 + (n+8) is a palindrome. under A027724. %N Palindromes of the form n^2 + (n+8). under A027725. More terms from Giovanni Resta, Aug 29, 2018. See Index Nrs 16 up to 19. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 20 up to 32. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 33 up to 41. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 42 up to 45. More terms from Patrick De Geest, Jun 22, 2023. See Index Nr 46. More terms from Patrick De Geest, Jul 18, 2023. See Index Nr 47. 2.024.980.892.661.756.697.013.490.002 4.100.547.615.645.204.997.648.623.368.633.268.467.994.025.465.167.450.014 291.110.773.714.896.523.959.619.515 84.745.482.572.885.688.920.872.755.855.727.802.988.658.827.528.454.748 28.871.285.875.858.590.001.229.569 833.551.148.125.551.710.375.568.181.865.573.017.155.521.841.155.338 21.483.563.234.526.184.866.880.587 461.543.489.251.885.190.477.082.818.280.774.091.588.152.984.345.164 2.928.331.740.489.196.140.653.250 8.575.126.782.356.484.771.760.148.410.671.774.846.532.876.215.758 2.159.210.693.397.915.883.253.487 4.662.190.818.483.908.709.229.276.729.229.078.093.848.180.912.664 2.958.418.939.805.275.953.670 8.752.242.623.398.572.986.568.656.892.758.933.262.422.578 2.855.744.435.294.488.382.589 8.155.276.279.715.436.344.590.954.436.345.179.726.725.518 2.146.566.864.566.595.055.807 46.076.865.807.219.121.234.843.212.191.270.856.867.064 214.655.225.436.557.032.432 46.076.865.807.219.121.234.843.212.191.270.856.867.064 29.927.294.176.812.473.509 895.642.936.745.473.786.434.687.374.547.639.246.598 29.201.685.813.894.053.374 852.738.454.373.381.202.454.202.183.373.454.837.258 28.627.570.794.205.246.685 819.537.809.577.233.218.474.812.332.775.908.735.918 21.453.822.714.860.484.567 460.266.509.080.663.692.515.296.366.080.905.662.064 20.362.349.579.179.647.037 414.625.280.384.717.548.797.845.717.483.082.526.414 2.919.019.406.760.380.374 8.520.674.297.043.722.974.792.273.407.924.760.258 2.896.827.497.610.422.905 8.391.609.550.911.864.724.274.681.190.559.061.938 204.899.512.505.754.537 41.983.810.225.095.860.106.859.052.201.838.914 29.293.314.111.168.350 858.098.251.615.574.808.475.516.152.890.858 28.989.019.759.841.184 840.363.266.636.462.646.264.636.662.363.048 21.622.406.372.184.972 467.528.457.323.905.303.509.323.754.825.764 21.459.803.444.244.992 460.523.163.865.629.242.926.568.361.325.064 2.989.063.335.060.290 8.934.499.621.001.746.471.001.269.944.398 2.930.792.062.562.649 8.589.542.113.980.229.220.893.112.459.858 Prime!    2.927.399.306.452.849 8.569.666.699.420.624.260.249.966.669.658 2.162.277.851.899.027 4.675.445.508.813.072.703.188.055.445.764 288.191.799.404.994 83.054.513.244.288.588.244.231.545.038 286.006.098.215.514 81.799.488.216.462.526.461.288.499.718 21.614.586.653.852 467.190.356.216.898.612.653.091.764 21.495.814.697.072 462.070.049.490.878.094.940.070.264 295.431.039.629 87.279.499.176.567.199.497.278 202.542.945.597 41.023.644.811.311.844.632.014 2.926.428.849 8.563.985.811.185.893.658 287.010.920 82.375.268.486.257.328 2.997.334 8.984.014.104.898 2.990.390 8.942.435.342.498 2.837.875 8.053.537.353.508 2.834.699 8.035.521.255.308 297.119 88.279.997.288 29.570 874.414.478 20.377 415.242.514 2.935 8.617.168 2.925 8.558.558 285 81.518 202 41.014 Prime!    29 878 0 8 [QM9] Case X = 9 One can find the regular numbers of the form n2+(n+9) at %N n^2 + (n+9). under A027694. The palindromic numbers of the form n2+(n+9) are categorised as follows : %N n^2 + (n+9) is a palindrome. under A027726. %N Palindromes of the form n^2 + (n+9). under A027727. More terms from Giovanni Resta, Aug 29, 2018. From Index Nrs 64 up to 71. More terms from Patrick De Geest, Sep 1, 2020. See Index Nrs 72 up to 117. More terms from Robert Xiao, Nov 11, 2022. See Index Nrs 118 up to 139. More terms from Robert Xiao, Dec 6, 2022. See Index Nrs 140 up to 164. More terms from Patrick De Geest, Jun 22, 2023. See Index Nr 165. More terms from Patrick De Geest, Jul 18, 2023. See Index Nrs 166 up to 170. 3.000.000.000.000.000.000.000.000.000 9.000.000.000.000.000.000.000.000.003.000.000.000.000.000.000.000.000.009 1.300.626.441.328.197.235.814.996.223 1.691.629.139.882.050.486.635.905.970.795.095.366.840.502.889.319.261.961 1.212.047.305.612.471.054.938.423.488 1.469.058.671.042.450.808.432.367.053.507.632.348.080.542.401.768.509.641 1.038.115.544.834.502.662.675.766.556 1.077.683.884.427.036.307.962.598.482.848.952.697.036.307.244.883.867.701 445.552.612.841.909.255.019.167.238 198.517.130.810.252.279.990.339.340.043.933.099.972.252.018.031.715.891 300.000.000.000.000.000.000.000.000 90.000.000.000.000.000.000.000.000.300.000.000.000.000.000.000.000.009 41.258.286.155.045.197.995.785.653 1.702.246.176.451.594.267.712.515.995.152.177.624.951.546.716.422.071 31.299.788.623.815.043.712.792.070 979.676.767.895.501.627.987.458.151.854.789.726.105.598.767.676.979 30.000.000.000.000.000.000.000.000 900.000.000.000.000.000.000.000.030.000.000.000.000.000.000.000.009 23.815.774.266.794.138.373.708.227 567.191.103.926.893.879.245.037.646.730.542.978.398.629.301.191.765 23.712.230.028.151.813.684.241.327 562.269.852.907.984.562.788.280.080.082.887.265.489.709.258.962.265 12.394.706.146.927.753.774.755.106 153.628.740.468.688.644.144.724.363.427.441.446.886.864.047.826.351 9.643.512.104.845.529.156.149.520 92.997.325.716.302.248.119.940.533.504.991.184.220.361.752.379.929 4.431.825.874.452.201.960.213.513 19.641.080.581.464.024.571.300.022.000.317.542.046.418.508.014.691 3.264.045.264.937.547.813.954.856 10.653.991.491.561.226.700.704.800.840.700.762.216.519.419.935.601 3.113.886.626.232.284.537.657.360 9.696.289.921.028.279.306.529.652.569.256.039.728.201.299.826.969 3.000.000.000.000.000.000.000.000 9.000.000.000.000.000.000.000.003.000.000.000.000.000.000.000.009 1.066.398.967.008.718.874.807.773 1.137.206.756.837.262.687.176.899.986.717.862.627.386.576.027.311 1.057.045.827.943.140.327.018.826 1.117.345.882.371.999.023.790.845.480.973.209.991.732.885.437.111 1.030.672.161.696.389.924.736.768 1.062.285.104.895.909.338.739.104.019.378.339.095.984.015.822.601 364.999.234.483.451.745.508.241 133.224.441.173.505.789.806.667.766.608.987.505.371.144.422.331 305.089.298.522.463.407.227.005 93.079.480.072.928.792.556.118.481.165.529.782.927.008.497.039 300.000.000.000.000.000.000.000 90.000.000.000.000.000.000.000.300.000.000.000.000.000.000.009 128.827.237.225.970.387.982.351 16.596.457.051.276.450.506.231.313.260.505.467.215.075.469.561 127.462.410.833.734.378.632.876 16.246.666.175.547.687.095.910.901.959.078.674.557.166.664.261 123.465.885.738.164.872.614.718 15.243.824.941.109.584.091.464.346.419.048.590.114.942.834.251 71.423.065.283.032.760.286.922 5.101.254.254.424.359.550.312.112.130.559.534.244.524.521.015 40.316.744.034.191.202.094.251 1.625.439.849.518.491.884.941.441.494.881.948.159.489.345.261 31.916.093.660.165.724.742.643 1.018.637.034.524.470.768.416.006.148.670.744.254.307.368.101 30.000.000.000.000.000.000.000 900.000.000.000.000.000.000.030.000.000.000.000.000.000.009 14.066.088.021.782.561.085.061 197.854.832.236.534.842.650.181.056.248.435.632.238.458.791 9.836.061.969.333.312.238.535 96.748.115.064.565.116.627.633.672.661.156.546.051.184.769 3.364.568.676.278.731.164.101 11.320.322.377.396.013.263.599.536.231.069.377.322.302.311 3.049.721.756.523.937.483.130 9.300.802.792.215.450.618.448.448.160.545.122.972.080.039 3.000.000.000.000.000.000.000 9.000.000.000.000.000.000.003.000.000.000.000.000.000.009 2.271.420.430.650.818.082.222 5.159.350.772.777.947.876.770.776.787.497.772.770.539.515 1.379.288.397.736.143.707.838 1.902.436.484.129.538.559.034.309.558.359.214.846.342.091 1.200.078.014.948.814.916.736 1.440.187.241.963.488.038.761.678.308.843.691.427.810.441 1.074.517.913.653.292.201.501 1.154.588.746.761.823.915.299.925.193.281.676.478.854.511 997.379.892.715.904.184.609 994.766.650.393.988.541.168.861.145.889.393.056.667.499 394.175.206.747.692.290.493 155.374.093.614.585.961.818.818.169.585.416.390.473.551 300.000.000.000.000.000.000 90.000.000.000.000.000.000.300.000.000.000.000.000.009 237.820.296.677.998.624.667 56.558.493.512.011.283.671.717.638.211.021.539.485.565 237.726.197.335.200.876.267 56.513.744.899.454.868.204.640.286.845.499.844.731.565 227.673.388.532.799.324.117 51.835.171.846.006.998.775.757.789.960.064.817.153.815 124.586.806.687.185.390.618 15.521.872.400.510.102.366.266.320.101.500.427.812.551 96.993.056.329.597.442.815 9.407.652.976.156.462.565.555.652.646.516.792.567.049 31.267.734.922.481.568.254 977.671.247.182.573.443.141.344.375.281.742.176.779 30.948.088.830.885.074.749 Prime!    957.784.202.284.353.512.838.215.353.482.202.487.759 30.886.706.212.236.486.274 953.988.620.641.007.953.111.359.700.146.026.889.359 30.000.000.000.000.000.000 900.000.000.000.000.000.030.000.000.000.000.000.009 22.761.453.140.953.328.317 518.083.749.087.814.135.252.531.418.780.947.380.815 12.356.255.930.003.019.281 152.677.060.607.734.778.929.877.437.706.060.776.251 9.520.691.133.001.233.975 90.643.559.650.008.320.288.202.380.005.695.534.609 3.897.012.554.826.686.293 15.186.706.852.476.816.644.661.867.425.860.768.151 3.422.795.298.433.113.901 11.715.527.654.975.829.255.292.857.945.672.551.711 3.069.325.912.785.429.984 9.420.761.558.896.112.951.592.116.988.551.670.249 3.027.632.478.680.776.510 9.166.558.425.962.702.631.362.072.695.248.556.619 3.000.000.000.000.000.000 9.000.000.000.000.000.003.000.000.000.000.000.009 2.383.224.109.158.209.827 5.679.757.154.472.942.831.382.492.744.517.579.765 1.407.464.140.369.542.238 1.980.955.306.426.174.497.944.716.246.035.590.891 1.390.255.830.520.081.738 1.932.811.274.295.082.238.322.805.924.721.182.391 1.158.845.561.992.536.066 1.342.923.036.549.796.751.576.979.456.303.292.431 1.085.720.773.447.473.973 1.178.789.597.895.381.106.011.835.987.959.878.711 968.166.647.234.714.830 937.346.656.817.708.749.947.807.718.656.643.739 403.850.324.398.604.048 163.095.084.516.857.724.427.758.615.480.590.361 300.000.000.000.000.000 90.000.000.000.000.000.300.000.000.000.000.009 136.883.299.310.520.483 18.737.037.630.133.537.473.533.103.673.073.781 100.101.032.507.332.343 10.020.216.709.034.006.560.043.090.761.202.001 31.159.467.620.387.045 970.912.422.385.948.727.849.583.224.219.079 30.000.000.000.000.000 900.000.000.000.000.030.000.000.000.000.009 22.788.502.426.511.662 519.315.842.843.127.929.721.348.248.513.915 13.718.360.536.465.216 188.193.415.808.446.222.644.808.514.391.881 11.731.882.304.045.041 137.637.062.395.965.191.569.593.260.736.731 11.578.846.113.932.066 134.069.677.330.119.717.911.033.776.960.431 3.262.179.310.062.143 10.641.813.850.997.522.579.905.831.814.601 3.000.000.000.000.000 9.000.000.000.000.003.000.000.000.000.009 1.411.031.348.053.413 1.991.009.465.189.433.349.815.649.001.991 1.361.700.097.732.883 1.854.227.156.165.744.475.616.517.224.581 1.325.889.400.817.846 1.757.982.703.201.108.011.023.072.897.571 1.006.850.261.673.268 1.013.747.449.431.529.251.349.447.473.101 951.322.744.355.124 905.014.963.927.365.563.729.369.410.509 370.656.884.454.041 137.386.525.993.176.671.399.525.683.731 302.985.210.998.585 91.800.038.083.857.375.838.083.000.819 300.207.281.032.100 90.124.411.584.686.568.648.511.442.109 300.000.000.000.000 90.000.000.000.000.300.000.000.000.009 41.989.656.355.546 1.763.131.240.856.886.580.421.313.671 41.944.248.388.153 1.759.319.972.847.117.482.799.139.571 30.000.000.000.000 900.000.000.000.030.000.000.000.009 14.016.755.641.638 196.469.438.717.404.717.834.964.691 12.977.693.492.548 168.420.528.386.535.683.825.024.861 12.389.095.521.106 153.489.687.831.101.138.786.984.351 11.270.747.729.271 127.029.754.376.878.673.457.920.721 Prime!    3.809.272.592.563 14.510.557.684.455.448.675.501.541 3.000.000.000.000 9.000.000.000.003.000.000.000.009 1.379.803.137.286 1.903.856.697.665.667.966.583.091 1.179.335.179.433 1.390.831.465.449.445.641.380.931 1.161.363.821.933 1.348.765.926.895.986.295.678.431 Prime!    720.082.209.317 518.518.388.175.571.883.815.815 300.000.000.000 90.000.000.000.300.000.000.009 226.596.191.582 51.345.834.039.693.043.854.315 225.969.524.077 51.062.225.811.811.852.226.015 107.716.960.201 11.602.943.515.051.534.920.611 30.000.000.000 900.000.000.030.000.000.009 11.950.115.336 142.805.256.555.652.508.241 11.430.454.733 130.655.295.414.592.556.031 Prime!    3.040.137.979 9.242.438.934.398.342.429 3.000.000.000 9.000.000.003.000.000.009 1.078.247.673 1.162.618.045.408.162.611 989.943.054 979.987.251.152.789.979 387.851.993 150.429.168.861.924.051 349.101.696 121.871.994.499.178.121 Prime!    346.313.573 119.933.091.190.339.911 337.310.898 113.778.642.246.877.311 302.382.689 91.435.290.909.253.419 300.000.000 90.000.000.300.000.009 128.536.648 16.521.670.007.612.561 120.588.436 14.541.571.017.514.541 109.666.003 12.026.632.323.662.021 98.066.439 9.617.026.556.207.169 Prime!    41.794.853 1.746.809.779.086.471 35.409.496 1.253.832.442.383.521 30.880.274 953.591.353.195.359 30.592.630 935.909.040.909.539 30.447.695 927.062.161.260.729 30.000.000 900.000.030.000.009 23.683.392 560.903.080.309.065 13.220.978 174.794.272.497.471 10.222.456 104.498.616.894.401 7.489.392 56.091.000.019.065 3.932.806 15.466.966.966.451 3.152.290 9.936.935.396.399 3.045.679 9.276.163.616.729 3.040.604 9.245.275.725.429 3.000.000 9.000.003.000.009 Prime!    2.378.507 5.657.297.927.565 989.154 978.426.624.879 980.560 961.498.894.169 963.304 927.955.559.729 315.165 99.329.292.399 300.000 90.000.300.009 128.348 16.473.337.461 125.206 15.676.667.651 114.141 13.028.282.031 Prime!    106.801 Prime!    11.406.560.411 72.062 5.193.003.915 30.605 936.696.639 30.000 900.030.009 9.854 97.111.179 Prime!    3.881 15.066.051 3.144 9.887.889 3.000 9.003.009 2.367 5.605.065 1.413 1.997.991 1.141 Prime!    1.303.031 969 939.939 438 192.291 Prime!    331 109.901 305 93.339 304 92.729 300 90.309 138 19.191 Prime!    31 1.001 30 939 22 515 Prime!    13 Prime!    191 Prime!    11 141 9 99 1 Prime!    11 0 9
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Further Topics Revealed

 Neil Sloane's "Integer Sequences" Encyclopedia can be consulted online : Neil Sloane's Integer Sequences If you are interested in the primes of these numbers rather than the palindromes, well look no further : %N n^2 + n + 1 is prime. under A002384 %N Primes of form n^2 + n + 1. under A002383 %N n^2 + n + 3 is prime. under A027752 %N Primes of form n^2 + n + 3. under A027753 %N n^2 + n + 5 is prime. under A027754 %N Primes of form n^2 + n + 5. under A027755 %N n^2 + n + 7 is prime. under A027756 %N Primes of form n^2 + n + 7. or [n^2 + 3n+9] under A005471 %N n^2 + n + 9 is prime. under A027757 %N Primes of form n^2 + n + 9. under A027758 Two more formula's are included in the table. They are well known to prime-lovers. n2 + n + 17 generates 16 primes for all n values 0 to 15 ! %N n^2 + n + 17 is prime. under A028823 %N n^2 + n + 17 is composite. under A007636 %N Primes of form n^2 + n + 17. under A007635 n2 + n + 41 generates 40 primes for all n values 0 to 39 ! %N n^2 + n + 41 is prime. under A002837 %N n^2 + n + 41 is composite. under A007634 %N Primes of form n^2 + n + 41. under A005846 Click here to view some of the author's [P. De Geest] entries to the table. Click here to view some entries to the table about palindromes.

Contributions

Copy & pasted from the OEIS Encyclopedia many more results from Giovanni Resta as indicated in the headings.

[ November 3, 2022 ]
Contribution from Robert Xiao (email)
“ I'm still working on some upgrades to the program, but in the meantime, I thought I'd share
the length-40 and length-41 entries for Case X = 2 [n^2 + n + 2] found by my program:

Length-40 took 229 seconds and length-41 took 689 seconds on my machine to generate.

Best,
Robert.”

[ November 11, 2022 ]
for Case X = 2 [n^2 + n + 2] entries [122] up to [128].
for Case X = 3 [n^2 + n + 3] entries [126] up to [188], except entry [167] which was already known.
for Case X = 4 [n^2 + n + 4] entries [58] up to [70].
for Case X = 5 [n^2 + n + 5] entries [80] up to [87].
for Case X = 6 [n^2 + n + 6] entries [55] up to [63].
for Case X = 7 [n^2 + n + 7] entries [72] up to [80].
for Case X = 8 [n^2 + n + 8] entries [33] up to [41].
for Case X = 9 [n^2 + n + 9] entries [118] up to [139].

[ December 6, 2022 ]
for Case X = 2 [n^2 + n + 2] entries [129] up to [152].
for Case X = 3 [n^2 + n + 3] entries [189] up to [316], except entry [286] which was already known.
for Case X = 4 [n^2 + n + 4] entries [71] up to [77].
for Case X = 5 [n^2 + n + 5] entries [88] up to [94].
for Case X = 6 [n^2 + n + 6] entries [64] up to [75].
for Case X = 7 [n^2 + n + 7] entries [81] up to [96].
for Case X = 8 [n^2 + n + 8] entries [42] up to [45].
for Case X = 9 [n^2 + n + 9] entries [140] up to [164].

[ June 22, 2023 ]
for Case X = 2 [n^2 + n + 2] entries [153] up to [155].
for Case X = 3 [n^2 + n + 3] entries [317] up to [352].
for Case X = 4 [n^2 + n + 4] entries [78] up to [81].
for Case X = 6 [n^2 + n + 6] entries [76] up to [78].
for Case X = 7 [n^2 + n + 7] entries [97] up to [99].
for Case X = 8 [n^2 + n + 8] entry [46].
for Case X = 9 [n^2 + n + 9] entry [165].

[ July 18, 2023 ]
for Case X = 2 [n^2 + n + 2] entries [156] up to [161].
for Case X = 3 [n^2 + n + 3] entries [353] up to [392].
for Case X = 4 [n^2 + n + 4] entry [82].
for Case X = 5 [n^2 + n + 5] entries [95] up to [97].
for Case X = 6 [n^2 + n + 6] entry [79].
for Case X = 7 [n^2 + n + 7] entries [100] up to [103].
for Case X = 8 [n^2 + n + 8] entry [47].
for Case X = 9 [n^2 + n + 9] entry [166] up to [170].

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