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A046118
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Smallest member of a sexy prime triple: value of p such that p, p+6 and p+12 are all prime, but p+18 is not (although p-6 might be).
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8
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7, 17, 31, 47, 67, 97, 101, 151, 167, 227, 257, 271, 347, 367, 557, 587, 607, 647, 727, 941, 971, 1097, 1117, 1181, 1217, 1277, 1291, 1361, 1427, 1447, 1487, 1607, 1657, 1747, 1777, 1867, 1901, 1987, 2131, 2281, 2377, 2411, 2677, 2687, 2707, 2791, 2897, 2957
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OFFSET
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1,1
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COMMENTS
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p-6 will be prime if the prime triple contains the last 3 primes of a sexy prime quadruple.
If a sexy prime triple happens to include the last 3 members of a sexy prime quadruple, this sequence will contain the sexy prime triple's smallest member; e.g., a(4)=47 is the smallest member of the sexy prime triple (47, 53, 59), but is also the second member of the sexy prime quadruple (41, 47, 53, 59). - Daniel Forgues, Aug 05 2009
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LINKS
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Eric M. Schmidt, Table of n, a(n) for n = 1..1000
Maxie D. Schmidt, New Congruences and Finite Difference Equations for Generalized Factorial Functions, arXiv:1701.04741 [math.CO], 2017.
Eric Weisstein's World of Mathematics, Sexy Primes.
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MATHEMATICA
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lst={}; Do[p=Prime[n]; If[PrimeQ[p+6]&&PrimeQ[p+12]&&!PrimeQ[p+18], AppendTo[lst, p]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 29 2008 *)
Select[Prime[Range[500]], AllTrue[#+{6, 12}, PrimeQ]&&CompositeQ[#+18]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 11 2019 *)
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PROG
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(PARI) lista(nn) = forprime(p=3, nn, if (isprime(p+6) && isprime(p+12) && !isprime(p+18), print1(p, ", ")); ); \\ Michel Marcus, Jan 06 2015
(MAGMA) [p: p in PrimesUpTo(5000) | not IsPrime(p+18) and IsPrime(p+6) and IsPrime(p+12)]; // Vincenzo Librandi, Sep 07 2017
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CROSSREFS
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Cf. A023201, A046117.
Cf. A046119, A046120.
Sequence in context: A290402 A001123 A094080 * A285738 A120092 A130284
Adjacent sequences: A046115 A046116 A046117 * A046119 A046120 A046121
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KEYWORD
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nonn
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AUTHOR
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Eric W. Weisstein
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EXTENSIONS
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Definition edited by Daniel Forgues, Aug 12 2009
More terms from Eric M. Schmidt, Sep 07 2017
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STATUS
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approved
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