# Find the pattern to this number series!

OK, so here is the series of numbers:

1225
1540
2926
4005
5985
8856
9045
9801
11781
11935
12376
12496
12720
13041
14400
16401
17200
17226
17290
17865
18096
21528
21736
23001
23751
24220
24976
25425
26796
27000


Whats the pattern? And what comes next? :)

• Did you make this yourself? – Mithical Jul 21 '16 at 9:36
• @Mithrandir I did. It comes from some research I have been doing into polygonal numbers, so thats a hint there. :) – pingu2k4 Jul 21 '16 at 9:41
• Just making sure, because if you post something that you didn't make yourself without attribution, it's plagiarism. :P – Mithical Jul 21 '16 at 9:49
• Once this is solved you should consider adding it to the OEIS. Probably best not to do that before it's solved, though. (Of course once I see the solution I may change my mind about its appropriateness for OEIS...) – Gareth McCaughan Jul 22 '16 at 9:24
• If my answer is correct then I think this (and some obvious "predecessors" to it) certainly do belong in OEIS. – Gareth McCaughan Jul 22 '16 at 10:05

These are (at least up to 27000) precisely the positive integers that

are polygonal numbers in at least seven ways.

I think the next number is

27405.

• Correct! I have the series calculated up to n = 3388, which gives all possible answers up to 2,500,000 so far, and have already submitted a pending addition to OEIS for these. :) oeis.org/A275256 is where I submitted these :) – pingu2k4 Jul 22 '16 at 10:43
• Did you also submit the corresponding sequences with (1) numbers below 7 and (2) exactly so many polygonal-number representations rather than at least so many? I think these should all be in OEIS. – Gareth McCaughan Jul 22 '16 at 11:52
• I haven't yet, can do in a short while though :) – pingu2k4 Jul 22 '16 at 14:44