

A046118


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 p6 might be).


8



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

1,1


COMMENTS

p6 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


LINKS

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.


MATHEMATICA

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 *)


PROG

(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


CROSSREFS

Cf. A023201, A046117.
Cf. A046119, A046120.
Sequence in context: A290402 A001123 A094080 * A285738 A120092 A130284
Adjacent sequences: A046115 A046116 A046117 * A046119 A046120 A046121


KEYWORD

nonn


AUTHOR

Eric W. Weisstein


EXTENSIONS

Definition edited by Daniel Forgues, Aug 12 2009
More terms from Eric M. Schmidt, Sep 07 2017


STATUS

approved



