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Search: id:A112021
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| A112021 |
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Number of partitions of n into Chen primes. |
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+0
5
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| 0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 14, 17, 19, 23, 26, 30, 35, 40, 46, 52, 60, 67, 77, 87, 98, 111, 124, 140, 157, 175, 197, 219, 244, 272, 302, 336, 372, 412, 456, 503, 556, 613, 675, 742, 816, 896, 983, 1078, 1180, 1291, 1411, 1542, 1683, 1836, 2001, 2178
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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a(n) = A000607 for n <= 42.
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MATHEMATICA
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(* first *) Needs["DiscreteMath`Combinatorica`"] (* then *) fQ[n_] := PrimeQ@n && (PrimeQ[n + 2] || 2 == Plus @@ Last /@ FactorInteger[n + 2]); f[n_] := Block[{c = k = 0, l = PartitionsP@n, p = Union /@ Partitions@n}, While[k++; k < l, If[Union[fQ /@ p[[k]]] == {True}, c++ ]]; c]; lst = {}; Do[ AppendTo[lst, f[n]], {n, 61}]; lst (* or *)
Rest@ CoefficientList[ Series[1/Times @@ (1 - x^Select[ Range@100, fQ@# &]), {x, 0, 61}], x] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jun 16 2006)
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CROSSREFS
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Cf. A112022, A101048, A109611.
Sequence in context: A027583 A029022 A140953 this_sequence A000607 A114372 A046676
Adjacent sequences: A112018 A112019 A112020 this_sequence A112022 A112023 A112024
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 26 2005
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