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Search: id:A118282
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| A118282 |
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Conjectured largest number that is not the sum of three generalized n-gonal numbers, or -1 if there is no largest number. |
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+0
4
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| 0, -1, 0, 0, 307, -1, 2027, 5200, 18180, -1, 10795, -1, 87740, -1, 75150, 212048, 122818, -1, 146970, 199153, 585513
(list; graph; listen)
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OFFSET
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3,5
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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 generalized n-gonal numbers. a(n)=0 for n=3 and 6 because generalized triangular and generalized hexagonal numbers are the same a triangular numbers, and 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. See A118283 for the number of numbers not representable.
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CROSSREFS
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Cf. A001318 (generalized pentagonal numbers), A085787 (generalized heptagonal numbers), A001082 (generalized octagonal numbers), A118277 (generalized 9-gonal numbers), A118278-A118285.
Sequence in context: A035843 A128477 A028680 this_sequence A050201 A142376 A142255
Adjacent sequences: A118279 A118280 A118281 this_sequence A118283 A118284 A118285
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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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