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Search: id:A116602
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| A116602 |
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Values of n such that p(2n) mod 12 == 5, where p(j) is the j-th prime. |
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8
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| 5, 8, 12, 13, 15, 20, 30, 31, 33, 49, 51, 52, 54, 58, 63, 70, 71, 74, 76, 79, 80, 81, 85, 88, 89, 92, 93, 97, 98, 103, 106, 109, 110, 117, 119, 126, 134, 135, 144, 145, 148, 149, 151, 156, 160, 165, 166, 169, 171, 175, 178, 181, 191, 192, 196, 199, 200, 201, 202, 204
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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These eight sets of integers (Editor's note: this and A116610-A116617) based on the {1,5,7,11} endings in modulo 12 comes from trying to construct sines and cosines using this sort of partitioning. f[n_Integer?Positive, 1] := If[Mod[Prime[n], 12] == 1, n!, 0] f[n_Integer?Positive, 2] := If[Mod[Prime[n], 12] == 5, n!, 0] f[n_Integer?Positive, 3] := If[Mod[Prime[n], 12] == 7, n!, 0] f[n_Integer?Positive, 4] := If[Mod[Prime[n], 12] == 11, n!, 0] CosM[x_, m_Integer?Positive] := Sum[If[f[2*n, m] == 0, 0, (-1)^n*x^(2*n)/f[2*n, m]], {n, 1, 200}] SinM[x_, m_Integer?Positive] := Sum[If[f[2*n + 1, m] == 0, 0, (-1)^n*x^(2* n + 1)/f[2*n + 1, m]], {n, 1, 200}]
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FORMULA
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A116602 = 1/2 * {even terms in A160591 = A000720(A040117)}. - M. F. Hasler, May 22 2009
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EXAMPLE
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33 is in the sequence because the 66-th prime is 317 and 317 mod 12=5.
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MAPLE
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a:=proc(n) if ithprime(2*n) mod 12 = 5 then n fi end: seq(a(n), n=1..220);
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MATHEMATICA
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a[1] = Flatten[Table[If[Mod[Prime[2*n], 12] == 5, n, {}], {n, 1, 100}]]
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PROGRAM
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(PARI) for(n=1, 999, prime(2*n)%12==5 & print1(n", ")) \\\\ M. F. Hasler, May 22 2009
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CROSSREFS
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Sequence in context: A133522 A133269 A076635 this_sequence A079896 A133315 A003658
Adjacent sequences: A116599 A116600 A116601 this_sequence A116603 A116604 A116605
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KEYWORD
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nonn,probation
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 29 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 05 2006, May 22 2009
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