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%I A046123 #27 Jan 25 2023 17:48:12
%S A046123 17,23,53,73,263,613,653,1103,1493,1613,1753,1873,2383,2683,3313,3923,
%T A046123 4013,5113,5393,5443,5653,6323,6373,9473,11833,12113,12653,13463,
%U A046123 14633,14753,15803,15913,17483,18223,19483,20353,21493,23333,24103
%N 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.
%C A046123 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
%H A046123 Amiram Eldar, <a href="/A046123/b046123.txt">Table of n, a(n) for n = 1..10000</a>
%H A046123 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 A046123 a(n) = A046122(n) + 6. - _Amiram Eldar_, Apr 22 2022
%t A046123 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 *)
%t A046123 Select[Prime[Range[3000]],AllTrue[#+{-12,-6,6},PrimeQ]&] (* _Harvey P. Dale_, Jan 25 2023 *)
%Y A046123 Cf. A023201, A046117.
%Y A046123 Cf. A023271, A046122, A046124.
%K A046123 nonn
%O A046123 1,1
%A A046123 _Eric W. Weisstein_

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