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Pa!indromic Sums of the first n 'type of numbers'
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	Sum of the first n primes is palindromic
	Sum of the first n odd primes is palindromic
	Sum of the first n composites is palindromic
	Sum of the first n odd composites is palindromic
	Sum of the first n even composites is palindromic
	Sum of the first n palindromes is palindromic
	Sum of the first n numbers is palindromic
	Sum of the first n odd numbers is palindromic
	Sum of the first n even numbers is palindromic

1. Sum of the first n primes is palindromic.

Sequence = 2 + 3 + 5 + 7 + 11 + 13 + ... + z
Index entries in OEIS A038582, A038584 and A038583
Other sources : Puzzle 7

Index	n	z	palindromic sum
1	1	2	2   Prime!
2	2	3	5   Prime!
3	8	19	77
4	7693	78347	285080582
5	8510	87641	352888253
6	12941	139241	854848458
7	146134	1959253	137372273731
8	637571	9564097	2939156519392
9	27198825	516916921	6833383883833386
10	53205635	1048924213	27155268786255172 by Jud McCranie
11	6283318531	155353386241	477749724515427947774 by Donovan Johnson
12	7167375533	178196630873	625179415050514971526 by Donovan Johnson
13	226095996998	6433462703963	714014821826628128410417 by Giovanni Resta
14	435966708249	12702232868389	2719564270866680724659172 by Giovanni Resta

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2. Sum of the first n odd primes is palindromic.

Sequence = 3 + 5 + 7 + 11 + 13 + 17 + ... + z
Index entries in OEIS A058845, A058846 and A058847

Index	n	z	palindromic sum
1	1	3	3   Prime!
2	2	5	8
3	49	229	5115
4	54	257	6336
5	172	1031	81218
6	921	7213	3091903   Prime Curios!
7	1421	11863	7843487   Prime Curios!
8	12485	133853	792727297
9	78653	1002073	37706560773
10	1969457	31924583	30398022089303
11	5606014	97137589	263888373888362
12	90638394	1837875227	81120957675902118 by Patrick De Geest

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3. Sum of the first n composites is palindromic.

Sequence = 4 + 6 + 8 + 9 + 10 + 12 + ... + z
Index entries in OEIS A053779, A057959 and A053780
Other sources : Puzzle 89

Index	n	z	palindromic sum
1	1	4	4
2	22	34	434
3	24	36	505
4	167	215	18781
5	202	258	27072
6	226	288	33633
7	1443	1711	1254521
8	2380	2785	3360633
9	3190	3708	5989895
10	3952	4572	9145419
11	4220	4873	10411401
12	16827	18986	161101161
13	26304	29509	390949093
14	37612	42005	795303597
15	40813	45534	935424539
16	213501	234272	25127372152
17	376524	411232	77753535777
18	1920079	2074123	1997671767991
19	2061085	2225480	2300809080032
20	2635057	2841251	3754911194573
21	3463613	3728941	6476856586746
22	4268588	4590401	9825337335289
23	16513206	17643216	146015161510641
24	68101132	72349270	2468348558438642
25	166428703	176262062	14693263036239641
26	207224360	219311147	22762189998126722
27	403784450	426454179	86234154745143268
28	421279478	444875288	93856121312165839
29	1384813481	1457527586	1010599968699950101
30	2758859588	2898662182	4003657190917563004
31	3921264376	4116490653	8080970392930790808
32	6249167674	6553235945	20500472188127400502 by Jeff Heleen

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4. Sum of the first n odd composites is palindromic.

Sequence = 9 + 15 + 21 + 25 + 27 + 33 + ... + z
Index entries in OEIS A058848, A058849 and A058850
Other sources : Puzzle 89

Index	n	z	palindromic sum
1	1	9	9
2	12	55	404
3	25	99	1441
4	61	215	7227
5	108	357	20802
6	211	663	73337
7	1344	3725	2576752
8	2339	6321	7576757   Prime Curios!
9	10539	26999	144666441
10	78409	191363	7584554857
11	283181	675861	96520502569
12	1748747	4073533	3584243424853
13	1795423	4180943	3776886886773
14	2386702	5540147	6651010101566
15	2819089	6531789	9260919190629
16	179101605	400974175	36028948184982063
17	1923088106	4248550291	4095836722276385904
18	2822581688	6224149881	8806146443446416088
19	7794689270	17109266357	66832347055074323866 by Jeff Heleen [ May 24, 2000 ]
20	17381011919	38023877981	331143864040468341133 by Donovan Johnson [ Sep 01, 2012 ]
21	25635268093	55995454633	719190811555118091917 by Donovan Johnson [ Sep 01, 2012 ]
22	28780043265	62836534343	906041488626884140609 by Chai Wah Wu [ Dec 06, 2019 ]
22	97973526253	212955815417	10450905369496350905401 by Chai Wah Wu [ Dec 06, 2019 ]

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5. Sum of the first n even composites is palindromic.

Sequence = 4 + 6 + 8 + 10 + 12 + 14 + ... + z
Index entries in OEIS A028553, A058851 and A028554

Aldo Palindromic numbers of the form n(n+3).
Main source see Palindromes of the form n(n+3)

The following substitution shows why the sequence equals x * (x + 3)

The sequence can be rewritten as 2 * (2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + ...)
The second term is 'the sum of the natural numbers' minus the starting number 1.
Replace it with the general formula we get 2 * [ (n^2 + n)/2 – 1 ] or [ n^2 + n – 2 ]
Substitute n with (x + 1) we get [ (x + 1)^2 + (x + 1) – 2 ] and work it out.
The sequence evolves from [ x^2 + 2x + 1 + x + 1 – 2 ] to [ x^2 + 3x ]
which finally yields to x * (x + 3) QED

Index	n	z	palindromic sum
1	1	4	4
2	8	18	88
3	28	58	868
4	66	134	4554
5	88	178	8008
6	211	424	45154
7	298	598	89698
8	671	1344	452254
9	2126	4254	4526254
10	2998	5998	8996998
11	28814	57630	830333038
12	29369	58740	862626268
13	29998	59998	899969998
14	63701	127404	4058008504
15	212206	424414	45032023054
16	212671	425344	45229592254
17	299998	599998	89999699998
18	636776	1273554	405485584504
19	2122206	4244414	4503764673054
20	2861419	5722840	8187727277818
21	2999998	5999998	8999996999998
22	9443423	18886848	89178266287198
23	21341691	42683384	455467838764554
24	28862883	57725768	833066101660338
25	29999998	59999998	899999969999998
26	212325206	424650414	45081993739918054
27	289053683	578107368	83552032523025538
28	294127328	588254658	86510885958801568
29	294174669	588349340	86538736763783568
30	299999998	599999998	89999999699999998 = Infinite pattern
Continued at Palindromes of the form n(n+3)

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6. Sum of the first n palindromes is palindromic.

Sequence = 1 + 2 + 3 + 4 + 5 + 6 + ... + z
Index entries in OEIS A046486 and A046487

Index	n	z	palindromic sum
1	1	1	1
2	2	2	3   Prime!
3	3	3	6
4	12	33	111
5	16	77	353   Prime!
6	47	383	7557
7	314	21512	2376732 by Patrick De Geest

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7. Sum of the first n numbers is palindromic.

Sequence = 1 + 2 + 3 + 4 + 5 + 6 + ... + z
Main source see Palindromic Triangulars

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8. Sum of the first n odd numbers is palindromic.

Sequence = 1 + 3 + 5 + 7 + 9 + 11 + ... + z
Main source see Palindromic Squares

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9. Sum of the first n even numbers is palindromic.

Sequence = 2 + 4 + 6 + 8 + 10 + 12 + ... + z
Main source see Palindromic Pronic Numbers

Enoch Haga (email) from California, USA.

Jeff Heleen (email) from New Hampshire, USA.

G. L. Honaker, Jr. (email) from Bristol, Virginia, USA.

Jud McCranie (email) from USA.

Carlos Rivera (email) from Monterrey, Nuevo León, México.

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Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com

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