%I A105414
%S A105414 17,71,149,191,431,521,821,1049,1277,1289,1451,1619,1667,1877,1949,2027,
%T A105414 2657,3299,3329,3467,3527,3539,3767,3929,4271,4931,5477,5849,6131,6659,
%U A105414 6701,6779,6827,8537,8819,8999,9419,9719,9929,10037,10091,11069,11117
%N 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.
%C A105414 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.
%e A105414 p(8)-2 = 17, p(8+6)-2 = 41, both prime, 17 is in the table.
%t A105414 For[n = 1, n < 500, n++, If[PrimeQ[Prime[n] + 2], If[PrimeQ[Prime[n + 
               7] - 2], Print[Prime[n]]]]] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Feb 07 2006
%o A105414 (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",") ) ) }
%Y A105414 Sequence in context: A043230 A044010 A106921 this_sequence A157910 A141959 
               A069496
%Y A105414 Adjacent sequences: A105411 A105412 A105413 this_sequence A105415 A105416 
               A105417
%K A105414 nonn
%O A105414 1,1
%A A105414 Cino Hilliard (hillcino368(AT)gmail.com), May 02 2005