[seqfan] Polygonal numbers

Daniel kimpire at yahoo.com
Sun Jul 24 12:28:20 CEST 2016

Hi all,

I am a long-time lurker on the OEIS site, and short-time lurker on the mailing list. I'm not a mathematician, but I enjoy exploring the integer sequences, particularly ones involving randomly selected three-digit numbers or ones that can have a physical or visual representation.

I come bearing a suggestion and question, related to each other.


First, the suggestion.

I was looking through one of my favorite sets of sequences, those related to polygonal numbers, and I got to wondering: is there a sequence that lists all non-trivially-polygonal numbers in ascending order (without repeats), and is there a sequence that lists all non-non-trivially-polygonal numbers?

Well, apparently there is: A090466 and A090467, respectively.

But I had the very devil of a time finding them. They are not cross-referenced from any of the single-n-gonal number sequences (triangular, rectangular, 27-gonal, 40-gonal, 100-gonal, etc.). Nor are they cross-referenced from the table-based all-n-polygonal sequences (such as A139600). It's not even in the index of sequences related to polygonal numbers at http://oeis.org/wiki/Index_to_OEIS:_Section_Pol!

In fact, I was *only* able to find A090466 by taking the contents of A139600, removing the first row and first two columns of the table in the Example, sequentially ordering the rest of the numbers, removing all duplicates, and searching for the sequence that resulted. 

Obviously A090466 should be added to http://oeis.org/wiki/Index_to_OEIS:_Section_Pol. I also suggest that cross-references to A090466 and A090467 be added to A139600, and probably all of the single-n-gonal number sequences as well. I'd do it myself, but I'm still hesitant to make the jump to actually submitting edits to the site.


Second, the question. 

Is there an equivalent to A090466 and A090467 for the centered polygonal numbers? I haven't been able to find one, nor have I been able to find an equivalent to A139600 that would enable me to build the sequence that would help me locate it.

Daniel Sterman

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