A105414 Numbers p(n) such that p(n)+2 and p(n+7)-2 are both prime numbers, where p(n) is the n-th prime.

17, 71, 149, 191, 431, 521, 821, 1049, 1277, 1289, 1451, 1619, 1667, 1877, 1949, 2027, 2657, 3299, 3329, 3467, 3527, 3539, 3767, 3929, 4271, 4931, 5477, 5849, 6131, 6659, 6701, 6779, 6827, 8537, 8819, 8999, 9419, 9719, 9929, 10037, 10091, 11069, 11117

Offset

1,1

Comments

Conjecture: There are an infinite number of primes p(n) such that p(n)-2 and p(n+k)-2 are both prime for all k > 1.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

p(8)-2 = 17, p(8+6)-2 = 41, both prime, 17 is in the sequence.

Mathematica

For[n = 1, n < 500, n++, If[PrimeQ[Prime[n] + 2], If[PrimeQ[Prime[n + 7] - 2], Print[Prime[n]]]]] (* Stefan Steinerberger, Feb 07 2006 *)
Select[Prime[Range[1500]], AllTrue[{#+2, Prime[PrimePi[#]+7]-2}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 05 2019 *)

Prog

(PARI) pnpk(n, m, k) = \ both are prime { local(x, l1, l2, v1, v2); for(x=1, n, v1 = prime(x)+ k; v2 = prime(x+m)+k; if(isprime(v1)&isprime(v2), \ print1(x", ") print1(v1", ") ) ) }

Crossrefs

Sequence in context: A043230 A044010 A106921 * A157910 A141959 A347334

Adjacent sequences: A105411 A105412 A105413 * A105415 A105416 A105417

Keyword

nonn

Author

Cino Hilliard, May 02 2005

Status

approved