A089007 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.

776117, 2157733, 4387067, 4814597, 5024039, 5437573, 5734693, 7249369, 9140429, 9394813, 9654977, 9654989, 12693013, 13632727, 14199319, 14848513, 15649133, 15677647, 18396449, 23659483, 23743943, 27724843, 28224293, 28677529

Offset

1,1

Links

Table of n, a(n) for n=1..24.

Example

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.

Mathematica

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 *)

Crossrefs

Subsequence of A088119.

For values of n see A089009: a(n) = A000040(A089009(n)).

Cf. A089492, A089524.

Sequence in context: A226113 A151562 A023348 * A252951 A145687 A244071

Adjacent sequences: A089004 A089005 A089006 * A089008 A089009 A089010

Keyword

nonn

Author

Pierre CAMI, Nov 03 2003

Extensions

Corrected and extended by Ray Chandler, Nov 04 2003

Entry revised by N. J. A. Sloane, Apr 01 2006

Status

approved