A109201 Minimal value of k>0 such that n^6 + k^2 is a semiprime.

2, 3, 1, 4, 1, 3, 7, 2, 5, 10, 1, 2, 5, 6, 5, 2, 7, 6, 11, 6, 3, 5, 3, 7, 11, 2, 3, 2, 9, 10, 7, 5, 5, 5, 5, 2, 1, 2, 5, 2, 3, 2, 5, 4, 9, 4, 3, 2, 5, 11, 3, 11, 3, 3, 5, 7, 1, 4, 3, 4, 11, 4, 5, 16, 7, 2, 7, 2, 3, 25, 9, 6, 5, 2, 5, 2, 5, 2, 5, 4, 17, 20, 7, 4, 5, 4, 15, 2, 5, 6, 7, 6, 3, 5, 1, 2, 5, 8, 3

Offset

0,1

Comments

It seems that one or more primes nearly always occur before finding the first such semiprime for a given n. There seems to be a high correlation with the n^5 + k^2 sequence (A109200) [such as n=63] and it with the n^2 + k^2 sequence (A109197).

Links

Table of n, a(n) for n=0..98.

Formula

a(n) = minimal value of k>0 such that n^6 + k^2 is semiprime.

Example

a(0) = 2 because 0^6 + 1^2 = 1 is not semiprime, but 0^6 + 2^2 = 4 = 2^2 is.
a(1) = 3 because 1^6 + 1^2 and 1^6 + 2^2 are not semiprime, but 1^6 + 3^2 = 10 = 2 * 5 is semiprime.
a(2) = 1 because 2^6 + 1^2 = 65 = 5 * 13 is semiprime.
a(69) = 25 because 69^6 + 25^2 = 107918163706 = 2 * 53959081853 and for no smaller k>0 is 69^6 + k^2 a semiprime.
a(100) = 7 because 100^6 + 7^2 = 1000000000049 = 6337 * 157803377 and for no smaller k>0 is 100^6 + k^2 a semiprime.

Crossrefs

Cf. A001358, A108714, A109197, A109198, A109199, A109200.

Sequence in context: A089555 A098554 A226081 * A002946 A286477 A277230

Adjacent sequences: A109198 A109199 A109200 * A109202 A109203 A109204

Keyword

easy,nonn

Author

Jonathan Vos Post, Jun 29 2005

Status

approved