A109202 Minimal value of k>0 such that n^7 + k^2 is a semiprime.

2, 3, 1, 2, 5, 6, 7, 4, 5, 8, 1, 6, 7, 5, 27, 16, 1, 12, 1, 2, 3, 8, 3, 6, 7, 2, 5, 2, 3, 12, 7, 4, 9, 2, 5, 6, 7, 4, 21, 2, 9, 4, 11, 6, 3, 4, 1, 2, 7, 25, 21, 14, 1, 4, 5, 4, 15, 8, 3, 22, 17, 8, 21, 10, 5, 2, 1, 14, 9, 32, 11, 6, 1, 13, 3, 2, 3, 3, 1, 2, 63, 4, 5, 10, 11, 9, 9, 4, 5, 33, 19, 6, 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^6 + k^2 sequence (A109201) with 24 times less than 100 the same values A109201(n) = A109202(n) for [n = 0,1,2,6,8,10,20,22,25,27,30,34,39,45,47,54,58,65,71,75,88,91,92,96].

Links

Table of n, a(n) for n=0..92.

Example

a(0) = 2 because 0^7 + 1^2 = 1 is not semiprime, but 0^7 + 2^2 = 4 = 2^2 is.
a(1) = 3 because 1^7 + 1^2 and 1^7 + 2^2 are not semiprime, but 1^7 + 3^2 = 10 = 2 * 5 is semiprime.
a(2) = 1 because 2^7 + 1^2 = 129 = 3 * 43 is semiprime.
a(80) = 63 because 80^7 + 63^2 = 20971520003969 = 47363 * 442782763 and for no smaller k>0 is 80^7 + k^2 a semiprime.
a(100) = 9 because 100^7 + 9^2 = 100000000000081 = 47309 * 2113762709 and for no smaller k>0 is 100^7 + k^2 a semiprime.

Mathematica

svk[n_]:=Module[{k=1, n7=n^7}, While[PrimeOmega[n7+k^2]!=2, k++]; k]; Array[ svk, 100, 0] (* Harvey P. Dale, Mar 01 2017 *)

Crossrefs

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

Sequence in context: A053452 A023986 A306732 * A362599 A245559 A117488

Adjacent sequences: A109199 A109200 A109201 * A109203 A109204 A109205

Keyword

easy,nonn

Author

Jonathan Vos Post, Jul 02 2005

Status

approved