A046119 Middle member of a sexy prime triple: value of p+6 such that p, p+6 and p+12 are all prime, but p+18 is not (although p-6 might be).

13, 23, 37, 53, 73, 103, 107, 157, 173, 233, 263, 277, 353, 373, 563, 593, 613, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1283, 1297, 1367, 1433, 1453, 1493, 1613, 1663, 1753, 1783, 1873, 1907, 1993, 2137, 2287, 2383, 2417, 2683, 2693, 2713

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

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 middle member; e.g., a(4)=53 is the middle member of the sexy prime triple (47, 53, 59), but is also the third member of the sexy prime quadruple (41, 47, 53, 59). - Daniel Forgues, Aug 05 2009

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• 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. A046118, A046120.

Programs

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[p+6]&&PrimeQ[p+12]&&!PrimeQ[p+18], AppendTo[lst, p+6]], {n, 7!}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 29 2008 *)
Select[Prime[Range[400]],And@@PrimeQ[{#-6,#+6}]&&!PrimeQ[#+12]&] (* Harvey P. Dale, Nov 01 2011 *)

Formula

a(n) = A046118(n) + 6. - Michel Marcus, Jan 06 2015

Extensions

Definition edited by Daniel Forgues, Aug 12 2009