A109197 Minimal value of k > 0 such that n^2 + k^2 is semiprime.

2, 3, 9, 1, 3, 1, 7, 3, 1, 1, 11, 1, 1, 3, 3, 1, 3, 3, 11, 1, 9, 2, 1, 2, 11, 1, 3, 4, 1, 1, 1, 2, 7, 5, 1, 1, 7, 4, 5, 1, 7, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 5, 2, 5, 4, 1, 1, 1, 1, 1, 2, 1, 1, 5, 7, 3, 1, 9, 1, 11, 4, 3, 2, 1, 2, 1, 1, 1, 14, 5, 2, 5, 1, 1, 5, 1, 6, 7, 2, 1, 2, 7, 1, 1, 6, 13, 8, 1

Offset: 0

Author

Jonathan Vos Post, Jun 21 2005

Keywords

• easy
• nonn

Examples

			a(0) = 2 because 0^2 + 1^2 = 1 is not semiprime, but 0^2 + 2^2 = 4 = 2^2 is.
a(1) = 3 because 1^2 + 1^2 and 1^2 + 2^2 are not semiprime, but 1^2 + 3^2 = 10 = 2 * 5 is semiprime.
a(81) = 14 because 81^2 + 14^2 = 6757 = 29 * 233 and for no smaller k>0 is 81^2 + k^2 a semiprime.
a(100) = 1 because 100^2 + 1^2 = 10001 = 73 * 137.
		

Crossrefs

Cf. A001358, A108714.

Programs

Mathematica

k2sp[n_]:=Module[{k=1},While[PrimeOmega[n^2+k^2]!=2,k++];k]; Array[ k2sp,110,0] (* Harvey P. Dale, Oct 30 2016 *)

PARI

A109197(n)={local(r);r=1;while(bigomega(n^2+r^2)<>2,r=r+1);r} \\ Michael B. Porter, May 13 2010

Formula

a(n) = minimal value of k > 0 such that n^2 + k^2 is semiprime.