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%I #3 Mar 30 2012 18:55:32
%S 5,8,12,4,2,6,20,22,8,8,12,22,26,30,20,20,74,52,22,26,4,22,6,42,40,8,
%T 58,44,42,8,40,6,36,28,2,28,6,4,20,14,2,12,8,46,2,40,10,4,110,12,18,
%U 44,42,6,24,20,8,28,46,2,18,6,60,36,24,2,18,4,24,48,6,30,6,6,22,6,2,6,2,40,2
%N Smallest k such that p(n)^5 + k is prime where p(n) is the n-th prime.
%e p(2)=3, 3^5 = 243; for odd k and n > 1, p(n)^r - k is even and thus not prime, so we only need consider even k.
%e for k = 2: 243 + 2 = 245, which is 5 * 7^2 and not prime.
%e for k = 4: 243 + 4 = 247, which is 13 * 19, also not prime.
%e for k = 6: 243 + 6 = 249, which is 3 * 83, also not prime.
%e for k = 8: 243 + 8 = 251, which is prime, so 8 is the smallest number that can be added to 243 to make another prime.
%e Hence a(2) = 8.
%Y Cf. A050997, A054271, A091666, A133517, A133518, A133519, A133520, A133521, (A001223).
%K easy,nonn
%O 1,1
%A _Carl R. White_, Sep 14 2007
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