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

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, 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, 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

Offset

0,1

Links

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

Example

a(0) = 2 because 0^10 + 1^2 = 1 is not semiprime, but 0^10 + 2^2 = 4 = 2^2 is.
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.
a(2) = 7 because 2^10 + 7^2 = 1073 = 29 * 37 is semiprime, but 2^10 plus no smaller square is.
a(99) = 56 because 99^10 + 56^2 = 90438207500880452137 = 3733 * 24226682963000389 and for no smaller k>0 is 99^10 + k^2 a semiprime.
a(100) = 17 because 100^10 + 17^2 = 100000000000000000289 = 181 *
552486187845303869 and for no smaller k>0 is 100^10 + k^2 a semiprime.

Mathematica

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 *)

Crossrefs

Cf. A001358, A108714, A109197, A109198, A109199, A109200, A109201, A109202, A109203, A109204.

Sequence in context: A358415 A245675 A245617 * A285294 A371258 A115630

Adjacent sequences: A109202 A109203 A109204 * A109206 A109207 A109208

Keyword

easy,nonn

Author

Jonathan Vos Post, Jul 05 2005

Status

approved