%I A105413
%S A105413 3,11,107,239,311,569,1019,1031,1229,1427,1997,2081,2087,2111,2687,3251,
%T A105413 4049,4127,4157,4229,4241,4481,5231,5639,6089,7307,7559,8969,9629,10007,
%U A105413 10457,13691,13829,13901,14249,14549,14561,16187,16649,17207
%N A105413 Numbers p(n) such that both p(n)+2 and p(n+6)-2 are prime numbers, where 
               p(n) is the n-th prime.
%C A105413 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 A105413 p(6)-2 = 11, p(6+5)-2 = 29, both prime, 1 is in the table.
%t A105413 For[n = 1, n < 500, n++, If[PrimeQ[Prime[n] + 2], If[PrimeQ[Prime[n + 
               6] - 2], Print[Prime[n]]]]] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Feb 07 2006
%o A105413 (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 A105413 Sequence in context: A007616 A121045 A092245 this_sequence A136985 A131546 
               A068693
%Y A105413 Adjacent sequences: A105410 A105411 A105412 this_sequence A105414 A105415 
               A105416
%K A105413 nonn
%O A105413 1,1
%A A105413 Cino Hilliard (hillcino368(AT)gmail.com), May 02 2005