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%I #21 Mar 07 2021 00:56:09
%S 13,23,37,53,73,103,107,157,173,233,263,277,353,373,563,593,613,653,
%T 733,947,977,1103,1123,1187,1223,1283,1297,1367,1433,1453,1493,1613,
%U 1663,1753,1783,1873,1907,1993,2137,2287,2383,2417,2683,2693,2713
%N 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).
%C p-6 will be prime if the prime triple contains the last 3 primes of a sexy prime quadruple.
%C 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
%H Harvey P. Dale, <a href="/A046119/b046119.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SexyPrimes.html">Sexy Primes</a>. [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].
%F a(n) = A046118(n) + 6. - _Michel Marcus_, Jan 06 2015
%t 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 *)
%t Select[Prime[Range[400]],And@@PrimeQ[{#-6,#+6}]&&!PrimeQ[#+12]&] (* _Harvey P. Dale_, Nov 01 2011 *)
%Y Cf. A023201, A046117.
%Y Cf. A046118, A046120.
%K nonn
%O 1,1
%A _Eric W. Weisstein_
%E Definition edited by _Daniel Forgues_, Aug 12 2009
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