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A231776 Least positive integer k <= n with (2^k + k) * n - 1 prime, or 0 if such a number k does not exist. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 16 07:19 EDT 2021. Contains 347469 sequences. (Running on oeis4.)