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

Offset: 3

Author

T. D. Noe, Apr 21 2006

Keywords

• sign

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

• 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).

Cf. A214419 (not the sum of three 10-gonal numbers).

Cf. A214420 (not the sum of three 11-gonal numbers).

Cf. A214421 (not the sum of three 12-gonal numbers).

Extensions

a(22)-a(33) from Donovan Johnson, Apr 17 2010