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Search: id:A117105
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| 3, 9, 15, 20, 21, 26, 32, 36, 37, 42, 43, 48, 53, 54, 57, 59, 63, 69, 70, 74, 75, 80, 83, 86, 89, 90, 91, 95, 96, 100, 102, 107, 111, 114, 116, 116, 116, 117, 120, 122, 123, 123, 126, 128, 133, 137, 143, 144, 147, 148, 149, 150, 153, 154, 156, 162, 163, 164, 165, 167
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Fermat discovered, Gauss, Legendre, and [1813] Cauchy proved that every integer is the sum of 7 heptagonal numbers (and there are some numbers which require all 7, the smallest being 13). 7 is the only prime heptagonal number. Primes which are sums of two positive heptagonal numbers include: {19, 41, 73, 89, 113, 149, 167, 193, 223, 229, 269, 293, 337, 347, 367, 383, 521, ...}. Primes which are sums of three positive heptagonal numbers include: {3, 37, 43, 53, 59, 83, 89, 107, 131, 137, 149, 163, 167, 173, 191, 197, 211, 227, 241, 251, 257, 263, 271, ...}.
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FORMULA
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{a(n)} = {A000566} + {A000566} + {A000566} = {a*(5*a-3)/2 + b*(5*b-3)/2 + c*(5*c-3)/2} \ {A000566}.
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CROSSREFS
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Cf. A000566, A000040, A000326, A003679, A064826, A117065.
Sequence in context: A071347 A093414 A123998 this_sequence A029506 A030594 A032676
Adjacent sequences: A117102 A117103 A117104 this_sequence A117106 A117107 A117108
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Apr 18 2006
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