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

Author

Zhi-Wei Sun, Nov 13 2013

Keywords

• nonn

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.

Examples

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

Links

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

Crossrefs

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

Programs

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 *)