A118278 - OEIS

A118278

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

0, -1, 33066, 146858, 273118, -1, 1274522, 2117145, 3613278, -1, 7250758, -1, 12911636, -1, 22655394, 26801303, 25049533, -1, 56922533, 115715602, 81539010, -1, 85105105, -1, 106555658, -1, 233296317, 267370631, 286763923, -1, 358322750

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OFFSET

3,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=3..33.

R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.

Gordon Pall, Large positive integers are sums of four or five values of a quadratic function, Am. J. Math 54 (1931) 66-78

Eric Weisstein's World of Mathematics, MathWorld: Polygonal Number

CROSSREFS

Cf. A118279 (number of numbers not representable).

Cf. A003679 (not the sum of three pentagonal numbers).

Cf. A007536 (not the sum of three hexagonal numbers).

Cf. A213523 (not the sum of three heptagonal numbers).

Cf. A213524 (not the sum of three octagonal numbers).

Cf. A213525 (not the sum of three 9-gonal numbers).