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A275681 Table read by rows: list of sexy prime triples (p, p+6, p+12) such that p+18 is composite.

%I A275681 #16 Sep 08 2022 08:46:17
%S A275681 7,13,19,17,23,29,31,37,43,47,53,59,67,73,79,97,103,109,101,107,113,
%T A275681 151,157,163,167,173,179,227,233,239,257,263,269,271,277,283,347,353,
%U A275681 359,367,373,379,557,563,569,587,593,599,607,613,619,647,653,659,727,733,739
%N A275681 Table read by rows: list of sexy prime triples (p, p+6, p+12) such that p+18 is composite.
%H A275681 Harvey P. Dale, <a href="/A275681/b275681.txt">Table of n, a(n) for n = 1..1000</a>
%H A275681 Wikipedia, <a href="http://en.wikipedia.org/wiki/Sexy_prime">Sexy prime</a>
%H A275681 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F A275681 a(3*n-2) = A046118(n).
%F A275681 a(3*n-1) = A046118(n)+6.
%F A275681 a(3*n) = A046118(n)+12.
%e A275681 The table starts:
%e A275681 7, 13, 19;
%e A275681 17, 23, 29;
%e A275681 31, 37, 43;
%e A275681 ...
%p A275681 N:= 10^4: # to get all entries <= N
%p A275681 Primes:= select(isprime,{seq(i,i=1..N+18,2)}):
%p A275681 S:= select(`<=`, Primes,N) intersect map(t -> t-6, Primes) intersect map(t -> t-12, Primes) minus map(t -> t-18, Primes):
%p A275681 map(t ->(t,t+6,t+12), sort(convert(S,list))); # _Robert Israel_, Aug 05 2016
%t A275681 Most[#]&/@Select[Table[n+{0,6,12,18},{n,Prime[Range[200]]}],PrimeQ[#] == {True,True,True,False}&]//Flatten (* _Harvey P. Dale_, Jan 19 2017 *)
%o A275681 (Magma) lst:=[]; for p in PrimesUpTo(727) do b:=p+6; if IsPrime(b) then c:=b+6; if IsPrime(c) and not IsPrime(c+6) then lst:=lst cat [p, b, c]; end if; end if; end for; lst;
%Y A275681 Cf. A023201 (sexy primes), A046118, A123082, A275682.
%K A275681 nonn,tabf
%O A275681 1,1
%A A275681 _Arkadiusz Wesolowski_, Aug 05 2016