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%I #7 Oct 01 2013 17:58:04
%S 5,7,11,59,11,13,41,17,23,43,23,29,53,31,67,53,37,59,41,43,97,53,103,
%T 53,79,59,83,149,67,167,71,127,89,113,83,89,101,149,311,97,101,109,
%U 101,107,113,127,137,131,157,137,127,149,137,163,137,281,193,149,229,191,157
%N First occurrence of primes p such that p = (prime(k) + prime(k+n))/2 for some positive integer k and n=2, 3, ...
%C No primes exist for n=1, as (prime(k) + prime(k+1))/2 is between prime(k) and prime(k+1) and so cannot be prime. See the Weisstein link.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Interprime.html">Interprime Numbers</a>
%e For n=2, (prime(2) + prime(2+2))/2 = (3+7)/2 = 5, so a(2)=5.
%e For n=4, (prime(2) + prime(2+4))/2 = (3+13)/2 = 8, which is not prime, but (prime(3) + prime(3+4))/2 = (5+17)/2 = 11, so a(4)=11.
%o (PARI) a(n) = {k=2;while(!isprime(p=(prime(k)+prime(k+n))/2),k++);p}
%K easy,nonn
%O 2,1
%A _Cino Hilliard_, Sep 10 2004
%E Edited by _Michael B. Porter_, Oct 07 2009
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