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
KEYWORD
nonn
AUTHOR
Cino Hilliard, May 02 2005
STATUS
approved