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%I #4 Mar 31 2012 10:22:00
%S 5,11,13,17,29,31,37,41,53,59,61,67,71,83,89,97,101,103,107,127,131,
%T 137,139,151,157,167,173,179,181,191,193,197,211,233,251,257,263,277,
%U 307,311,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421
%N Primes prime(n) such that there exists a 0 < k < n-1 such that prime(n+k) + prime(n-k) = 2*prime(n).
%C prime(11+3) + prime(11-3) = 2*prime(11); therefore prime(11) = 31 is in the sequence.
%t a = {}; For[k = 3, k < 100, k++, For[n = 1, n < k - 1, n++, If[(Prime[k + n] + Prime[k - n])/2 == Prime[k], AppendTo[a, Prime[k]]]]]; Union[a, a]
%K nonn
%O 1,1
%A _Artur Jasinski_, Dec 23 2006
%E Edited, corrected and extended by _Stefan Steinerberger_, Jul 31 2007
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