Here are a few random examples : 535, 3773, 246191642
Palindromic Products of Two Sequential Integers are defined and calculated by this extraordinary intricate and excruciatingly complex formula. So, this line is for experts only :
In you are interested in case n = 1 then visit this page about palindromic pronic numbers !
In case of n = 2 note that the formula n(n+2) can be written also as n2+2n.
Its always easier to refer something by name so I'll baptise these numbers Palindromic Quasipronic Numbers.
A repetitive infinite palindromic pattern can be made in the following manner :
9 x 11 = 99
99 x 101 = 9999
999 x 1001 = 999999
9999 x 10001 = 99999999
So far I compiled 59 Palindromic Quasipronic Numbers.
Here is the largest non trivial one that I discovered on [May 6, 2000 ].
This nonpalindromic basenumber
6.035.200.088.907
has 13 digits
yielding the following palindromic quasipronic number
36.423.640.113.155.131.104.632.463
with a length of 26 digits.
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Palindromic Quasipronic Numbers can only end in one of the following digits : 3, 4, 5, 8 or 9.
Warut Roonguthai (email) from Bangkok Thailand informed me that every (palindromic) number
of the form n(n+2) is also of the form n^21.
" It's just one step away from being a palindromic square. And that is why I think that it is interesting to investigate palindromes of the form n^2+1 , another near miss, as well. "
Proof that numbers of the form n^21 equal n(n+2) by substituting n with m+1 :
n^2 1 =
(m + 1)^2 1 =
m^2 + 2m + 1 1 =
m^2 + 2m =
m(m + 2) QED
A finite palindromic pattern hides in the list in the following manner :
2 x 4 = 8
2966 x 2968 = 8803088
2967032 x 2967034 = 8803284823088
2967032966 x 2967032968 = 8803284627264823088
2967032967032 x 2967032967034 = 8803284627460647264823088
Note that the lengths of the resulting palindromes increases with steps of 6 !
Sources Revealed

Neil Sloane's "Integer Sequences" Encyclopedia can be consulted online :
Neil Sloane's Integer Sequences
The regular quasipronic numbers are categorised as follows :
%N n(n+2) under A005563 .
Check out the following two entries about Palindromic Quasipronic Numbers
%N n(n+2) is a palindrome under A028503.
%N Palindromes of form n(n+2) under A028504.
Click here to view some the author's [P. De Geest] entries to the table.
Click here to view some entries to the table about palindromes.
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The Table

My program completed the search upto length 26 inclusive.
| Index Nr | Info |
Basenumber | Length |
| Palindromic Product of Sequence n(n+2) | Length |
| | | |
Twofold sequence (n) x (n+2) Palindromic Quasipronic Numbers |
| 59 |
9.999.999.999.999 | 13 |
| 99.999.999.999.999.999.999.999.999 | 26 |
| 58 |
6.035.200.088.907 | 13 |
| 36.423.640.113.155.131.104.632.463 | 26 |
| 57 |
3.153.099.043.049 | 13 |
| 9.942.033.575.282.825.753.302.499 | 25 |
| 56 |
2.967.841.885.466 | 13 |
| 8.808.085.457.132.317.545.808.088 | 25 |
| 55 |
2.967.032.967.032 | 13 |
| 8.803.284.627.460.647.264.823.088 | 25 |
| 54 |
2.939.136.124.286 | 13 |
| 8.638.521.157.088.807.511.258.368 | 25 |
| 53 |
2.839.531.502.896 | 13 |
| 8.062.939.155.944.495.519.392.608 | 25 |
| 52 |
2.050.695.871.494 | 13 |
| 4.205.353.557.366.637.553.535.024 | 25 |
| 51 |
999.999.999.999 | 12 |
| 999.999.999.999.999.999.999.999 | 24 |
| 50 |
186.125.268.237 | 12 |
| 34.642.615.476.667.451.624.643 | 23 |
| 49 |
178.923.207.531 | 12 |
| 32.013.514.193.539.141.531.023 | 23 |
| 48 |
99.999.999.999 | 11 |
| 9.999.999.999.999.999.999.999 | 22 |
| 47 |
64.819.595.894 | 11 |
| 4.201.580.011.991.100.851.024 | 22 |
| 46 |
54.809.426.001 | 11 |
| 3.004.073.178.668.713.704.003 | 22 |
| 45 |
31.519.410.879 | 11 |
| 993.473.262.222.262.374.399 | 21 |
| 44 |
24.064.405.175 | 11 |
| 579.095.596.474.695.590.975 | 21 |
| 43 |
18.511.102.337 | 11 |
| 342.660.909.767.909.066.243 | 21 |
| 42 |
18.163.818.617 | 11 |
| 329.924.306.787.603.429.923 | 21 |
| 41 |
9.999.999.999 | 10 |
| 99.999.999.999.999.999.999 | 20 |
| 40 |
3.146.471.489 | 10 |
| 9.900.282.837.382.820.099 | 19 |
| 39 |
2.967.032.966 | 10 |
| 8.803.284.627.264.823.088 | 19 |
| 38 |
2.441.052.185 | 10 |
| 5.958.735.774.775.378.595 | 19 |
| 37 |
999.999.999 | 9 |
| 999.999.999.999.999.999 | 18 |
| 36 |
185.812.387 | 9 |
| 34.526.243.534.262.543 | 17 |
| 35 |
99.999.999 | 8 |
| 9.999.999.999.999.999 | 16 |
| 34 |
93.809.716 | 8 |
| 8.800.263.003.620.088 | 16 |
| 33 |
31.552.659 | 8 |
| 995.570.353.075.599 | 15 |
| 32 |
22.765.895 | 8 |
| 518.286.020.682.815 | 15 |
| 31 |
9.999.999 | 7 |
| 99.999.999.999.999 | 14 |
| 30 |
9.200.156 | 7 |
| 84.642.888.824.648 | 14 |
| 29 |
2.967.032 | 7 |
| 8.803.284.823.088 | 13 |
| 28 |
1.868.287 | 7 |
| 3.490.500.050.943 | 13 |
| 27 |
999.999 x 1.000.001 | 6-7 |
| 999.999.999.999 | 12 |
| 26 |
552.101 x 552.103 | 6 |
| 304.816.618.403 | 12 |
| 25 |
293.786 x 293.788 | 6 |
| 86.310.801.368 | 11 |
| 24 |
243.063 x 243.065 | 6 |
| 59.080.108.095 | 11 |
| 23 |
179.317 x 179.319 | 6 |
| 32.154.945.123 | 11 |
| 22 |
174.747 x 174.749 | 6 |
| 30.536.863.503 | 11 |
| 21 |
174.601 x 174.603 | 6 |
| 30.485.858.403 | 11 |
| 20 |
99.999 x 100.001 | 5-6 |
| 9.999.999.999 | 10 |
| 19 |
20.564 x 20.566 | 5 |
| 422.919.224 | 9 |
| 18 |
18.991 x 18.993 | 5 |
| 360.696.063 | 9 |
| 17 |
9.999 x 10.001 | 4-5 |
| 99.999.999 | 8 |
| 16 |
5.731 x 5.733 | 4 |
| 32.855.823 | 8 |
| 15 |
2.966 x 2.968 | 4 |
| 8.803.088 | 7 |
| 14 |
2.365 x 2.367 | 4 |
| 5.597.955 | 7 |
| 13 |
1.907 x 1.909 | 4 |
| 3.640.463 | 7 |
| 12 |
1.747 x 1.749 | 4 |
| 3.055.503 | 7 |
| 11 |
999 x 1.001 | 3-4 |
| 999.999 | 6 |
| 10 |
204 x 206 | 3 |
| 42.024 | 5 |
| 9 |
191 x 193 | 3 |
| 36.863 | 5 |
| 8 |
99 x 101 | 2-3 |
| 9.999 | 4 |
| 7 |
75 x 77 | 2 |
| 5.775 | 4 |
| 6 |
64 x 66 | 2 |
| 4.224 | 4 |
| 5 |
23 x 25 | 2 |
| 575 | 3 |
| 4 |
17 x 19 | 2 |
| 323 | 3 |
| 3 |
9 x 11 | 1-2 |
| 99 | 2 |
| 2 |
2 x 4 | 1 |
| 8 | 1 |
| 1 |
1 x 3 | 1 |
| 3 | 1 |
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