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Search: id:A121861
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| A121861 |
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Least previously nonoccurring positive integer such that partial sum + 1 is prime. |
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+0
4
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| 1, 3, 2, 4, 6, 12, 8, 10, 14, 18, 22, 26, 24, 16, 30, 32, 28, 20, 34, 36, 42, 44, 46, 62, 52, 38, 60, 48, 58, 56, 54, 40, 50, 64, 68, 72, 76, 84, 66, 96, 74, 70, 80, 100, 86, 78, 88, 104, 90, 106, 122, 112, 98, 102, 94, 92, 118, 114, 108, 110, 124, 116, 138, 82, 120, 128, 150
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = {1,3} UNION {permutation of even positive numbers}. The corresponding partial sums + 1 are 2, 5, 7, 13, 17, 29, 37, 47, 61, 79, 101, 127, 151, ...,.
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FORMULA
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a(n) = MIN{k>0 such that 1 + k + SUM[i=1..n-1]a(i) is prime and k <> a(i)}.
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EXAMPLE
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a(1) = 1 because 1+1 = 2 is prime.
a(2) = 3 because 1+3+1 = 5 is prime.
a(3) = 2 because 1+3+2+1 = 7 is prime.
a(4) = 4 because 1+3+2+4+1 = 11 is prime.
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MATHEMATICA
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f[s_] := Append[s, k = 1; p = 1 + Plus @@ s; While[MemberQ[s, k] || ! PrimeQ[p + k], k++ ]; k]; Nest[f, {}, 67] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A000040, A121862.
Sequence in context: A114745 A039915 A085346 this_sequence A060006 A123097 A134571
Adjacent sequences: A121858 A121859 A121860 this_sequence A121862 A121863 A121864
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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), Aug 30 2006
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EXTENSIONS
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Corrected and extended by Robert G. Wilson v, Aug 31 2006
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