%I #7 Jun 16 2016 16:58:46
%S 2,3,1,2,7,3,5,16,3,4,1,10,1,2,3,8,1,2,5,10,3,2,1,8,5,4,9,2,9,3,13,8,
%T 15,8,7,2,5,2,3,16,3,9,31,14,3,4,3,10,11,2,3,2,9,12,5,4,3,10,5,6,11,6,
%U 9,16,5,28,19,4,3,16,3,6,7,4,9,28,9,6,11,12,7,10,7,14,29,3,11,8,3,18,7,8,3,4
%N Minimal value of k>0 such that n^5 + k^2 is a semiprime.
%F a(n) = minimal value of k>0 such that n^5 + k^2 is a semiprime.
%e a(0) = 2 because 0^5 + 1^2 = 1 is not semiprime, but 0^5 + 2^2 = 4 = 2^2 is.
%e a(1) = 3 because 1^5 + 1^2 and 1^5 + 2^2 are not semiprime, but 1^5 + 3^2 = 10 = 2 * 5 is semiprime.
%e a(2) = 1 because 2^5 + 1^2 = 33 = 3 * 11 is semiprime.
%e a(42) = 31 because 42^5 + 31^2 = 130692193 = 571 * 228883 and for no smaller k>0 is 42^4 + k^2 a semiprime.
%t a[n_] := (For[k = 1, PrimeOmega[n^5 + k^2] != 2, k++]; k); a /@ Range[0, 93] (* _Giovanni Resta_, Jun 16 2016 *)
%Y Cf. A001358, A108714, A109197, A109198, A109199.
%K easy,nonn
%O 0,1
%A _Jonathan Vos Post_, Jun 26 2005
%E a(46) corrected by _Giovanni Resta_, Jun 16 2016
|