A109198 Minimal value of k > 0 such that n^3 + k^2 is semiprime.

2, 3, 1, 8, 1, 2, 1, 8, 5, 4, 9, 4, 11, 2, 13, 2, 1, 12, 1, 12, 7, 5, 1, 2, 5, 3, 3, 10, 1, 18, 7, 4, 3, 2, 5, 2, 7, 2, 7, 2, 7, 6, 1, 2, 5, 7, 3, 4, 11, 2, 3, 16, 5, 2, 11, 2, 9, 2, 1, 40, 1, 4, 5, 8, 5, 9, 17, 2, 7, 5, 1, 6, 1, 4, 3, 14, 3, 4, 1, 18, 9, 10, 3, 6, 5, 3, 15, 4, 9, 3, 7, 10, 11, 2, 3, 12

Offset

0,1

Comments

When n+1 and n^2+1 are both prime, then k=1.

Links

Table of n, a(n) for n=0..95.

Formula

a(n) = minimal value of k > 0 such that n^3 + k^2 is semiprime.

Example

a(0) = 2 because 0^3 + 1^2 = 1 is not semiprime, but 0^3 + 2^2 = 4 = 2^2 is.
a(1) = 3 because 1^3 + 1^2 and 1^3 + 2^2 are not semiprime, but 1^3 + 3^2 = 10 = 2 * 5 is semiprime.
a(59) = 40 because 59^3 + 40^2 = 206979 = 3 * 68993 and for no smaller k > 0 is 59^3 + k^2 a semiprime.
a(100) = 1 because 100^3 + 1^2 = 1000001 = 101 * 9901.

Mathematica

k2sp[n_]:=Module[{n3=n^3, k=1}, While[PrimeOmega[n3+k^2]!=2, k++]; k]; Array[ k2sp, 100, 0] (* Harvey P. Dale, Oct 15 2013 *)

Prog

(PARI) A109198(n)={local(r); r=1; while(bigomega(n^3+r^2)<>2, r=r+1); r} \\ Michael B. Porter, May 14 2010

Crossrefs

Cf. A001358, A108714, A109197.

Sequence in context: A192363 A097710 A171024 * A081320 A147865 A266614

Adjacent sequences: A109195 A109196 A109197 * A109199 A109200 A109201

Keyword

easy,nonn

Author

Jonathan Vos Post, Jun 22 2005

Status

approved