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A263311 Numbers n such that each of p=6*n+1, q=6*p+1, r=6*q+1 and s=6*r+1 is prime.

%I A263311 #25 Oct 27 2015 18:05:57
%S A263311 10,1060,1795,1885,2965,3245,3335,4065,4325,5015,5875,6985,7605,7905,
%T A263311 9785,11315,12045,12360,14390,14970,15285,15500,15885,17195,18220,
%U A263311 20670,20695,22160,24915,25645,25955,26025,29410,29910,32925,35530,36280
%N A263311 Numbers n such that each of p=6*n+1, q=6*p+1, r=6*q+1 and s=6*r+1 is prime.
%C A263311 Each p is a starting prime of a complete generalized Cunningham chain p(k)=6*p(k-1)+1.
%C A263311 All terms are multiples of 5. Hence t = 6s+1 = 1555+7776n are always composite, and the chains are indeed "complete."
%C A263311 Subsequence of A263310 (and as such of A263309 and of A024899).
%H A263311 Zak Seidov, <a href="/A263311/b263311.txt">Table of n, a(n) for n = 1..20000</a>
%H A263311 Wikipedia, <a href="http://en.wikipedia.org/wiki/Cunningham_chain">Cunningham chain</a>
%p A263311 isA263311 := proc(n)
%p A263311     return isprime(6*n+1) and isprime(36*n+7) and isprime(216*n+43) and isprime(1296*n+259) ;
%p A263311 end proc:
%p A263311 for n from 1 to 30000 do
%p A263311     if isA263311(n) then
%p A263311         printf("%d,",n);
%p A263311     end if;
%p A263311 end do; # _R. J. Mathar_, Oct 17 2015
%t A263311 Select[Range[10,100000,5],PrimeQ[p=6*#+1]&&PrimeQ[q=6*p+1]&&PrimeQ[r=6*q+1]&&PrimeQ[s=6*r+1]&]
%o A263311 (PARI) for(n=1, 1e5, if(isprime(p=6*n+1) && isprime(q=6*p+1) && isprime(r=6*q+1) && isprime(6*r+1), print1(n", "))) \\ _Altug Alkan_, Oct 17 2015
%Y A263311 Cf. A024899, A263309, A263310.
%K A263311 nonn
%O A263311 1,1
%A A263311 _Zak Seidov_, Oct 13 2015