A046123 Third member of a sexy prime quadruple: value of p+12 such that p, p+6, p+12 and p+18 are all prime.

17, 23, 53, 73, 263, 613, 653, 1103, 1493, 1613, 1753, 1873, 2383, 2683, 3313, 3923, 4013, 5113, 5393, 5443, 5653, 6323, 6373, 9473, 11833, 12113, 12653, 13463, 14633, 14753, 15803, 15913, 17483, 18223, 19483, 20353, 21493, 23333, 24103

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

Is 17 the only term that is not equal to 3 mod 10? It is the only such term up to the one millionth prime. - Harvey P. Dale, Jan 25 2023

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• 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].

Crossrefs

Cf. A023201, A046117.

Cf. A023271, A046122, A046124.

Programs

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[p+6]&&PrimeQ[p+12]&&PrimeQ[p+18], AppendTo[lst, p+12]], {n, 8!}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 29 2008 *)
Select[Prime[Range[3000]],AllTrue[#+{-12,-6,6},PrimeQ]&] (* Harvey P. Dale, Jan 25 2023 *)

Formula

a(n) = A046122(n) + 6. - Amiram Eldar, Apr 22 2022