cp's OEIS Frontend

A109199 Minimal value of k>0 such that n^4 + k^2 is semiprime.

%I A109199 #6 Nov 21 2013 12:48:43
%S A109199 2,3,3,1,3,1,7,1,1,14,1,1,1,1,1,2,3,1,1,5,17,1,1,1,17,2,1,10,9,1,1,4,
%T A109199 1,4,5,1,1,6,1,1,1,5,1,4,5,7,5,6,13,5,1,14,1,4,5,2,3,1,1,14,7,1,1,4,7,
%U A109199 1,5,4,1,16,3,1,1,1,3,4,5,6,1,10,7,1,9,4,1,3,1,16,3,4,31,15,1,4,1,3,5,6,1,4
%N A109199 Minimal value of k>0 such that n^4 + k^2 is semiprime.
%H A109199 Harvey P. Dale, <a href="/A109199/b109199.txt">Table of n, a(n) for n = 0..1000</a>
%F A109199 a(n) = minimal value of k>0 such that n^4 + k^2 is semiprime.
%e A109199 a(0) = 2 because 0^4 + 1^2 = 1 is not semiprime, but 0^4 + 2^2 = 4 = 2^2 is.
%e A109199 a(1) = 3 because 1^4 + 1^2 and 1^4 + 2^2 are not semiprime, but 1^4 + 3^2 = 10 = 2 * 5 is semiprime.
%e A109199 a(90) = 31 because 90^4 + 31^2 = 65610961 = 13 * 5046997 and for no smaller k>0 is 90^4 + k^2 a semiprime.
%e A109199 a(100) = 1 because 100^4 + 1^2 = 100000001 = 17 * 5882353.
%t A109199 n4sp[n_]:=Module[{k=1,n4=n^4},While[PrimeOmega[n4+k^2]!=2,k++];k]; Array[n4sp,100,0] (* _Harvey P. Dale_, Dec 03 2011 *)
%Y A109199 Cf. A001358, A108714, A109197, A109198.
%K A109199 easy,nonn
%O A109199 0,1
%A A109199 _Jonathan Vos Post_, Jun 22 2005