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Search: id:A118278
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| A118278 |
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Conjectured largest number that is not the sum of three n-gonal numbers, or -1 if there is no largest number. |
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+0
9
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| 0, -1, 33066, 146858, 273118, -1, 1274522, 2117145, 3613278, -1, 7250758, -1, 12911636, -1, 22655394, 26801303, 25049533, -1, 56922533
(list; graph; listen)
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OFFSET
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3,3
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COMMENT
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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.
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REFERENCES
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R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.
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LINKS
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Eric Weisstein's World of Mathematics, MathWorld: Polygonal Number
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CROSSREFS
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Cf. A118279 (number of numbers not representable), A003679 (not the sum of three pentaagonal numbers), A007536 (not the sum of three hexagonal numbers).
Sequence in context: A083603 A045061 A132992 this_sequence A118280 A062682 A094889
Adjacent sequences: A118275 A118276 A118277 this_sequence A118279 A118280 A118281
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KEYWORD
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sign
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Apr 21 2006
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