

A118278


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


16



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 ngonal 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), 169172.
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 9gonal numbers).
Cf. A214419 (not the sum of three 10gonal numbers).
Cf. A214420 (not the sum of three 11gonal numbers).
Cf. A214421 (not the sum of three 12gonal numbers).
Sequence in context: A170789 A237625 A237624 * A118280 A062682 A094889
Adjacent sequences: A118275 A118276 A118277 * A118279 A118280 A118281


KEYWORD

sign


AUTHOR

T. D. Noe, Apr 21 2006


EXTENSIONS

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


STATUS

approved



