A231776 Least positive integer k <= n with (2^k + k) * n - 1 prime, or 0 if such a number k does not exist.

1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 6, 2, 10, 1, 2, 1, 2, 1, 2, 1, 4, 2, 2, 1, 2, 8, 6, 1, 2, 1, 4, 2, 2, 1, 8, 1, 4, 1, 2, 2, 14, 2, 2, 1, 2, 1, 2, 6, 2, 1, 4, 2, 2, 3, 8, 1, 6, 1, 2, 1, 8, 5, 4, 1, 2, 1, 2, 6, 42, 2, 6, 2, 4, 2, 2, 1, 2, 1, 4, 1, 4, 2, 8, 1, 2, 1, 2, 1, 6, 1, 8, 20, 2, 1, 2, 6, 10, 1, 2, 2

Offset

1,3

Comments

We find that 75011 is the only value of n <= 10^5 with a(n) = 0. The least positive integer k with (2^k + k)*75011 - 1 prime is 81152.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

a(3) = 2 since (2^1 + 1) * 3 - 1 = 8 is not prime, but (2^2 + 2) * 3 - 1 = 17 is prime.

Mathematica

Do[Do[If[PrimeQ[(2^k+k)*n-1], Print[n, " ", k]; Goto[aa]], {k, 1, n}]; Print[n, " ", 0]; Label[aa]; Continue, {n, 1, 100}]
lpi[n_]:=Module[{k=1}, While[!PrimeQ[n(2^k+k)-1], k++]; k]; Array[lpi, 100] (* Harvey P. Dale, Aug 10 2019 *)

Crossrefs

Cf. A000040, A000079, A231201, A231557, A231561, A231725.

Sequence in context: A161299 A161274 A160978 * A055734 A295660 A193169

Adjacent sequences: A231773 A231774 A231775 * A231777 A231778 A231779

Keyword

nonn

Author

Zhi-Wei Sun, Nov 13 2013

Status

approved