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Search: id:A078465
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| A078465 |
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Primonacci numbers: a(n)=a(n-2)+a(n-3)+a(n-5)+a(n-7)+a(n-11)+...+a(n-p(k))+... until n > p(k), where p(k) is the k-th prime. a(1)=a(2)=1. |
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+0
2
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| 1, 1, 1, 2, 2, 4, 5, 8, 12, 16, 26, 36, 55, 81, 118, 177, 257, 384, 564, 833, 1233, 1813, 2685, 3956, 5845, 8629, 12731, 18807, 27746, 40976, 60481, 89282, 131816, 194562, 287253, 424018, 625968, 924077
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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a(n)/a(n-1) -> 1.476229...=1/x, where x satisfies the Sum x^p(n)=1 equation, i.e. x^2+x^3+x^5+x^7+x^11+... =1. (What constant is it?)
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..500
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EXAMPLE
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a(12)=36=a(12-2)+a(12-3)+a(12-5)+a(12-7)+a(12-11)=a(10)+a(9)+a(7)+a(5)+a(1)=16+12+5+2+1=36
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CROSSREFS
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Cf. A078974 (the constant 1.47622...), A084256 (the constant 1/1.47622...)
Sequence in context: A006206 A095719 A050364 this_sequence A094992 A079501 A093335
Adjacent sequences: A078462 A078463 A078464 this_sequence A078466 A078467 A078468
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Miklos Kristof (kristofmiki(AT)freemail.hu), Jan 02 2003
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