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A109205 Minimal value of k>0 such that n^10 + k^2 is a semiprime.

%I A109205 #7 Aug 01 2021 12:46:07
%S A109205 2,3,7,4,1,4,5,2,5,10,3,2,11,7,9,8,1,10,7,4,7,4,5,2,5,3,1,20,3,9,7,2,
%T A109205 7,5,21,4,5,2,3,4,3,4,25,3,3,13,31,2,7,24,7,2,5,2,1,4,9,7,5,4,23,9,17,
%U A109205 8,29,8,17,2,3,10,13,2,13,7,5,4,11,8,5,10,17,4,21,5,31,4,5,4,13,2,7,4,25
%N A109205 Minimal value of k>0 such that n^10 + k^2 is a semiprime.
%H A109205 Harvey P. Dale, <a href="/A109205/b109205.txt">Table of n, a(n) for n = 0..1000</a>
%e A109205 a(0) = 2 because 0^10 + 1^2 = 1 is not semiprime, but 0^10 + 2^2 = 4 = 2^2 is.
%e A109205 a(1) = 3 because 1^10 + 1^2 and 1^10 + 2^2 are not semiprime, but 1^10 + 3^2 = 10 = 2 * 5 is semiprime.
%e A109205 a(2) = 7 because 2^10 + 7^2 = 1073 = 29 * 37 is semiprime, but 2^10 plus no smaller square is.
%e A109205 a(99) = 56 because 99^10 + 56^2 = 90438207500880452137 = 3733 * 24226682963000389 and for no smaller k>0 is 99^10 + k^2 a semiprime.
%e A109205 a(100) = 17 because 100^10 + 17^2 = 100000000000000000289 = 181 *
%e A109205 552486187845303869 and for no smaller k>0 is 100^10 + k^2 a semiprime.
%t A109205 mvk[n_]:=Module[{c=n^10,k=1},While[PrimeOmega[c+k^2]!=2,k++];k]; Array[ mvk,100,0] (* _Harvey P. Dale_, Aug 01 2021 *)
%Y A109205 Cf. A001358, A108714, A109197, A109198, A109199, A109200, A109201, A109202, A109203, A109204.
%K A109205 easy,nonn
%O A109205 0,1
%A A109205 _Jonathan Vos Post_, Jul 05 2005