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%I #10 Mar 14 2015 16:42:54
%S 776117,2157733,4387067,4814597,5024039,5437573,5734693,7249369,
%T 9140429,9394813,9654977,9654989,12693013,13632727,14199319,14848513,
%U 15649133,15677647,18396449,23659483,23743943,27724843,28224293,28677529
%N Sequence of primes p(n) such that 2*p(n)+3, 2*p(n+1)+3, 2*p(n+2)+3, 2*p(n+3)+3 are four consecutive primes, where p(i) denotes the i-th prime.
%e 776117 is in the sequence because it is the 62178th prime, followed by the primes 776119, 776137 and 776143; and 2*776117+3 = 1552237, 2*776119+3 = 1552241, 2*776137+3 = 1552277 and 2*776143+3 = 1552289 which are the 117814th, 117815th, 117816th and 117817th prime respectively.
%t lst = {}; Do[ If[ PrimeQ[2Prime[n] + 3], If[ PrimeQ[2Prime[n + 1] + 3], If[ PrimeQ[2Prime[n + 2] + 3], If[ PrimeQ[2Prime[n + 3] + 3], If[ PrimePi[2Prime[n] + 3] + 3 == PrimePi[2Prime[n + 3] + 3], AppendTo[lst, Prime[n]]] ]]]], {n, 2048081}] (* _Robert G. Wilson v_, Jan 13 2005 *)
%Y Subsequence of A088119.
%Y For values of n see A089009: a(n) = A000040(A089009(n)).
%Y Cf. A089492, A089524.
%K nonn
%O 1,1
%A _Pierre CAMI_, Nov 03 2003
%E Corrected and extended by _Ray Chandler_, Nov 04 2003
%E Entry revised by _N. J. A. Sloane_, Apr 01 2006
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