A109203 Minimal value of k>0 such that n^8 + k^2 is a semiprime.

2, 3, 3, 14, 3, 2, 1, 5, 7, 1, 1, 4, 5, 1, 3, 7, 1, 10, 1, 11, 1, 4, 1, 6, 13, 3, 1, 20, 1, 4, 11, 4, 1, 1, 1, 16, 5, 5, 1, 4, 3, 6, 1, 1, 15, 4, 5, 1, 17, 4, 1, 1, 1, 1, 11, 4, 1, 14, 1, 10, 1, 14, 7, 4, 15, 4, 1, 4, 1, 1, 1, 9, 1, 15, 9, 8, 9, 10, 5, 14, 3, 1, 5, 6, 1, 3, 19, 14, 5, 6, 41, 4, 1, 14, 1

Offset: 0

Author

Jonathan Vos Post, Jul 03 2005

Keywords

• easy
• nonn

Comments

There seems to be a modest correlation with the n^7 sequence (A109202) with often the same values [n = 10,16,18,23,31,45,52,55,66,72,82,88,100]. Sometimes the same value of k occurs for the n^6 sequence (A109201), the n^7 sequence (A109202) and this n^8 sequence, for instance n=88, k=5. The statistics of these sequences is unclear, as are the asymptotics.

Examples

			a(0) = 2 because 0^8 + 1^2 = 1 is not semiprime, but 0^8 + 2^2 = 4 = 2^2 is.
a(1) = 3 because 1^8 + 1^2 and 1^8 + 2^2 are not semiprime, but 1^8 + 3^2 = 10 = 2 * 5 is semiprime.
a(2) = 3 because 2^8 + 3^2 = 265 = 5 * 53 is semiprime, but 2^8 + 1^2 and 2^8 + 2^2 are not semiprimes.
a(90) = 41 because 90^8 + 41^2 = 4304672100001681 = 6317 * 681442472693 and for no smaller k>0 is 90^8 + k^2 a semiprime.
a(100) = 9 because 100^8 + 9^2 = 10000000000000081 = 34361 * 291027618521 and for no smaller k>0 is 100^8 + k^2 a semiprime.
		

Crossrefs

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