0,1

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).

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

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.

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

Sequence in context: A035612 A089555 A098554 this_sequence A002946 A035426 A065516

Adjacent sequences: A109198 A109199 A109200 this_sequence A109202 A109203 A109204

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Jun 29 2005