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A275682 Table read by rows: list of sexy prime quadruples (p, p+6, p+12, p+18) such that p+24 is composite.

%I A275682 #21 Nov 19 2024 02:41:36
%S A275682 11,17,23,29,41,47,53,59,61,67,73,79,251,257,263,269,601,607,613,619,
%T A275682 641,647,653,659,1091,1097,1103,1109,1481,1487,1493,1499,1601,1607,
%U A275682 1613,1619,1741,1747,1753,1759,1861,1867,1873,1879,2371,2377,2383,2389
%N A275682 Table read by rows: list of sexy prime quadruples (p, p+6, p+12, p+18) such that p+24 is composite.
%C A275682 (5, 11, 17, 23, 29) is a sexy prime 5-tuple and this is the only sexy prime 5-tuple.
%C A275682 Essentially same as A123083.
%H A275682 Vincenzo Librandi, <a href="/A275682/b275682.txt">Table of n, a(n) for n = 1..2100</a>
%H A275682 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sexy_prime">Sexy prime</a>
%H A275682 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F A275682 a(n) = A123083(n+4).
%e A275682 The table starts:
%e A275682 11, 17, 23, 29;
%e A275682 41, 47, 53, 59;
%e A275682 61, 67, 73, 79;
%e A275682 ...
%t A275682 Most[#]&/@Select[Table[n + {0, 6, 12, 18, 24}, {n, Prime[Range[200]]}], PrimeQ[#]=={True, True, True, True, False}&]//Flatten (* _Vincenzo Librandi_, Jun 09 2017 *)
%t A275682 #+{0,6,12,18}&/@Select[Prime[Range[400]],AllTrue[#+{6,12,18},PrimeQ] && CompositeQ[#+24]&]//Flatten (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Apr 29 2019 *)
%o A275682 (Magma) lst:=[]; for p in PrimesInInterval(7, 2371) do b:=p+6; if IsPrime(b) then c:=b+6; if IsPrime(c) then d:=c+6; if IsPrime(d) then lst:=lst cat [p, b, c, d]; end if; end if; end if; end for; lst;
%Y A275682 Cf. A023201, A023271, A123083, A275681.
%K A275682 nonn,tabf
%O A275682 1,1
%A A275682 _Arkadiusz Wesolowski_, Aug 05 2016