A109200 Minimal value of k>0 such that n^5 + k^2 is a semiprime.

2, 3, 1, 2, 7, 3, 5, 16, 3, 4, 1, 10, 1, 2, 3, 8, 1, 2, 5, 10, 3, 2, 1, 8, 5, 4, 9, 2, 9, 3, 13, 8, 15, 8, 7, 2, 5, 2, 3, 16, 3, 9, 31, 14, 3, 4, 3, 10, 11, 2, 3, 2, 9, 12, 5, 4, 3, 10, 5, 6, 11, 6, 9, 16, 5, 28, 19, 4, 3, 16, 3, 6, 7, 4, 9, 28, 9, 6, 11, 12, 7, 10, 7, 14, 29, 3, 11, 8, 3, 18, 7, 8, 3, 4

Offset

0,1

Links

Table of n, a(n) for n=0..93.

Formula

a(n) = minimal value of k>0 such that n^5 + k^2 is a semiprime.

Example

a(0) = 2 because 0^5 + 1^2 = 1 is not semiprime, but 0^5 + 2^2 = 4 = 2^2 is.
a(1) = 3 because 1^5 + 1^2 and 1^5 + 2^2 are not semiprime, but 1^5 + 3^2 = 10 = 2 * 5 is semiprime.
a(2) = 1 because 2^5 + 1^2 = 33 = 3 * 11 is semiprime.
a(42) = 31 because 42^5 + 31^2 = 130692193 = 571 * 228883 and for no smaller k>0 is 42^4 + k^2 a semiprime.

Mathematica

a[n_] := (For[k = 1, PrimeOmega[n^5 + k^2] != 2, k++]; k); a /@ Range[0, 93] (* Giovanni Resta, Jun 16 2016 *)

Crossrefs

Cf. A001358, A108714, A109197, A109198, A109199.

Sequence in context: A138507 A209579 A205699 * A158909 A199915 A209557

Adjacent sequences: A109197 A109198 A109199 * A109201 A109202 A109203

Keyword

easy,nonn

Author

Jonathan Vos Post, Jun 26 2005

Extensions

a(46) corrected by Giovanni Resta, Jun 16 2016

Status

approved