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A136721 Prime quadruples: 3rd term.

%I A136721 #17 Oct 11 2019 15:54:22
%S A136721 11,17,107,197,827,1487,1877,2087,3257,3467,5657,9437,13007,15647,
%T A136721 15737,16067,18047,18917,19427,21017,22277,25307,31727,34847,43787,
%U A136721 51347,55337,62987,67217,69497,72227,77267,79697,81047,82727,88817,97847
%N A136721 Prime quadruples: 3rd term.
%C A136721 Primes p such that p-6, p-4, and p+2 are prime. Apart from the first term, a(n) = 17 (mod 30).
%C A136721 The members of each quadruple are twin primes when they are 1st and 2nd terms and when 3rd and 4th terms. When they are 2nd and 3rd terms they differ by 4.
%H A136721 Robert Israel, <a href="/A136721/b136721.txt">Table of n, a(n) for n = 1..10000</a>
%F A136721 a(n) = A007530(n)+6 = A136720(n)+4 = A090258(n)-2. - _Robert Israel_, Oct 11 2019
%e A136721 The four terms in the first quadruple are 5,7,11,13 and in the 2nd 11,13,17,19. The four terms or members of each set must be simultaneously prime.
%p A136721 p2:= 0: p3:= 0: p4:= 0:
%p A136721 Res:= NULL: count:= 0:
%p A136721 while count < 100 do
%p A136721   p1:= p2; p2:= p3; p3:= p4;
%p A136721   p4:= nextprime(p4);
%p A136721   if [p2-p1, p3-p2, p4-p3] = [2, 4, 2] then
%p A136721      count:= count+1; Res:= Res, p3
%p A136721   fi
%p A136721 od:
%p A136721 Res; # _Robert Israel_, Oct 11 2019
%t A136721 lst={};Do[p0=Prime[n];If[PrimeQ[p2=p0+2], If[PrimeQ[p6=p0+6], If[PrimeQ[p8=p0+8], AppendTo[lst, p6]]]], {n, 12^4}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 22 2008 *)
%Y A136721 Cf. A007530, A090258, A136720.
%K A136721 easy,nonn
%O A136721 1,1
%A A136721 _Enoch Haga_, Jan 18 2008
%E A136721 Edited by _Charles R Greathouse IV_, Oct 11 2009