This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A090467 #59 Feb 16 2025 08:32:51
%S A090467 1,2,3,4,5,7,8,11,13,14,17,19,20,23,26,29,31,32,37,38,41,43,44,47,50,
%T A090467 53,56,59,61,62,67,68,71,73,74,77,79,80,83,86,89,97,98,101,103,104,
%U A090467 107,109,110,113,116,119,122,127,128,131,134,137,139,140,143,146,149,151,152
%N A090467 Numbers which are not regular figurative or polygonal numbers of order greater than 2. That is, numbers not of the form 1 + k*m*(m-1)/2 - (m-1)^2 where k > 2 and m > 2.
%C A090467 The m-th k-gonal number is 1 + k*m*(m-1)/2 - (m-1)^2 = A057145(k,m).
%C A090467 Numbers that are strictly trivially polygonal: numbers m that are only 2-gonal and m-gonal. - _Daniel Mondot_, Jun 13 2024
%D A090467 Albert H. Beiler, Recreations In The Theory Of Numbers, The Queen Of Mathematics Entertains, Dover, NY, 1964, pp. 185-199.
%H A090467 Michel Marcus, <a href="/A090467/b090467.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H A090467 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FigurateNumber.html">Figurate Number</a>.
%H A090467 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%F A090467 An integer n >= 3 is in this sequence iff A176774(n) = n (or, equivalently, A176775(n) = 2). - _Max Alekseyev_, Apr 24 2018
%e A090467 3 is a triangular number, but is not a k-gonal number for any other k, so 3 is a term.
%e A090467 6 is both a triangular number and a hexagonal number, so 6 is not a term.
%t A090467 Complement[ Table[i, {i, 300}], Take[ Union[ Flatten[ Table[1 + k*n(n - 1)/2 - (n - 1)^2, {n, 3, 40}, {k, 3, 300}]]], 300]]
%o A090467 (PARI) isok(n) = (n < 3) || (vecsum(vector(n-2, k, k+=2; ispolygonal(n, k))) == 1); \\ _Michel Marcus_, May 01 2016
%Y A090467 Complement is A090466.
%Y A090467 Cf. A057145, A176774, A176775.
%K A090467 easy,nonn
%O A090467 1,2
%A A090467 _Robert G. Wilson v_, Dec 01 2003
%E A090467 Verified by _Don Reble_, Mar 12 2006