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

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, 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, 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

Offset

0,1

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

a(n) = minimal value of k>0 such that n^4 + k^2 is semiprime.

Example

a(0) = 2 because 0^4 + 1^2 = 1 is not semiprime, but 0^4 + 2^2 = 4 = 2^2 is.
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.
a(90) = 31 because 90^4 + 31^2 = 65610961 = 13 * 5046997 and for no smaller k>0 is 90^4 + k^2 a semiprime.
a(100) = 1 because 100^4 + 1^2 = 100000001 = 17 * 5882353.

Mathematica

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 *)

Crossrefs

Cf. A001358, A108714, A109197, A109198.

Sequence in context: A295634 A317665 A329315 * A279813 A256909 A343533

Adjacent sequences: A109196 A109197 A109198 * A109200 A109201 A109202

Keyword

easy,nonn

Author

Jonathan Vos Post, Jun 22 2005

Status

approved