cp's OEIS Frontend

A118278 Conjectured largest number that is not the sum of three n-gonal numbers, or -1 if there is no largest number.

%I A118278 #19 Feb 16 2025 08:33:01
%S A118278 0,-1,33066,146858,273118,-1,1274522,2117145,3613278,-1,7250758,-1,
%T A118278 12911636,-1,22655394,26801303,25049533,-1,56922533,115715602,
%U A118278 81539010,-1,85105105,-1,106555658,-1,233296317,267370631,286763923,-1,358322750
%N A118278 Conjectured largest number that is not the sum of three n-gonal numbers, or -1 if there is no largest number.
%C A118278 Extensive calculations show that if a(n) >= 0, then every number greater than a(n) can be represented as the sum of three n-gonal numbers. a(3)=0 because every number can be written as the sum of three triangular numbers. When n is a multiple of 4, there is an infinite set of numbers not representable. For n=14, there appears to be a sparse, but infinite, set of numbers not representable.
%H A118278 R. K. Guy, <a href="http://www.jstor.org/stable/2324367">Every number is expressible as the sum of how many polygonal numbers?</a>, Amer. Math. Monthly 101 (1994), 169-172.
%H A118278 Gordon Pall, <a href="https://doi.org/2371077">Large positive integers are sums of four or five values of a quadratic function</a>, Am. J. Math 54 (1931) 66-78
%H A118278 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">MathWorld: Polygonal Number</a>
%Y A118278 Cf. A118279 (number of numbers not representable).
%Y A118278 Cf. A003679 (not the sum of three pentagonal numbers).
%Y A118278 Cf. A007536 (not the sum of three hexagonal numbers).
%Y A118278 Cf. A213523 (not the sum of three heptagonal numbers).
%Y A118278 Cf. A213524 (not the sum of three octagonal numbers).
%Y A118278 Cf. A213525 (not the sum of three 9-gonal numbers).
%Y A118278 Cf. A214419 (not the sum of three 10-gonal numbers).
%Y A118278 Cf. A214420 (not the sum of three 11-gonal numbers).
%Y A118278 Cf. A214421 (not the sum of three 12-gonal numbers).
%K A118278 sign
%O A118278 3,3
%A A118278 _T. D. Noe_, Apr 21 2006
%E A118278 a(22)-a(33) from _Donovan Johnson_, Apr 17 2010