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 p-6 might be).

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

Offset

1,1

Comments

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

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. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- N. J. A. Sloane, Mar 07 2021].

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 *)
Select[Prime[Range[500]], AllTrue[#+{6, 12}, PrimeQ]&&CompositeQ[#+18]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 11 2019 *)

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