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%I #5 Mar 01 2017 09:14:29
%S 2,3,1,2,5,6,7,4,5,8,1,6,7,5,27,16,1,12,1,2,3,8,3,6,7,2,5,2,3,12,7,4,
%T 9,2,5,6,7,4,21,2,9,4,11,6,3,4,1,2,7,25,21,14,1,4,5,4,15,8,3,22,17,8,
%U 21,10,5,2,1,14,9,32,11,6,1,13,3,2,3,3,1,2,63,4,5,10,11,9,9,4,5,33,19,6,3
%N Minimal value of k>0 such that n^7 + k^2 is a semiprime.
%C It seems that one or more primes nearly always occur before finding the first such semiprime for a given n. There seems to be a high correlation with the n^6 + k^2 sequence (A109201) with 24 times less than 100 the same values A109201(n) = A109202(n) for [n = 0,1,2,6,8,10,20,22,25,27,30,34,39,45,47,54,58,65,71,75,88,91,92,96].
%e a(0) = 2 because 0^7 + 1^2 = 1 is not semiprime, but 0^7 + 2^2 = 4 = 2^2 is.
%e a(1) = 3 because 1^7 + 1^2 and 1^7 + 2^2 are not semiprime, but 1^7 + 3^2 = 10 = 2 * 5 is semiprime.
%e a(2) = 1 because 2^7 + 1^2 = 129 = 3 * 43 is semiprime.
%e a(80) = 63 because 80^7 + 63^2 = 20971520003969 = 47363 * 442782763 and for no smaller k>0 is 80^7 + k^2 a semiprime.
%e a(100) = 9 because 100^7 + 9^2 = 100000000000081 = 47309 * 2113762709 and for no smaller k>0 is 100^7 + k^2 a semiprime.
%t svk[n_]:=Module[{k=1,n7=n^7},While[PrimeOmega[n7+k^2]!=2,k++];k]; Array[ svk,100,0] (* _Harvey P. Dale_, Mar 01 2017 *)
%Y Cf. A001358, A108714, A109197, A109198, A109199, A109200, A109201.
%K easy,nonn
%O 0,1
%A _Jonathan Vos Post_, Jul 02 2005
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