A102748 a(n) is the least k such that (2^n)*(10^k) -1 or +1 is prime.

0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 4554, 1, 1, 0, 1, 2, 0, 0, 2, 0, 2, 2, 3, 6, 1, 12, 21, 14, 4, 5, 74, 0, 3, 2, 5, 12, 7, 2, 1, 5, 16, 3, 1870, 5, 24, 22, 10, 1, 22, 20, 2, 19, 10, 1, 1, 1196, 9, 4, 10, 29, 34, 0, 2, 187, 3, 46, 29, 62, 62, 22, 2622, 1, 38, 2, 1, 172

Offset

0,11

Comments

For n even >2 the least prime is of the form (2^n)*(10^k)+1. For n odd >2 the least prime is of the form (2^n)*(10^k)-1 Mersenne-primes are in the sequence with a(n)=0 and n prime.

Links

Table of n, a(n) for n=0..75.

Example

(2^0)*(10^0)+1 = 2 prime so a(0) = 0.
(2^1)*(10^0)+1 = 3 prime so a(1) = 0.
(2^2)*(10^0)-1 = 3 prime as (2^2)*(10^0)+1 = 5 prime so a(2) = 0.

Mathematica

a[n_] := Module[{k=0}, While[!PrimeQ[2^n*10^k - 1] && !PrimeQ[2^n*10^k + 1], k++]; k]; Array[a, 10, 0] (* Amiram Eldar, Aug 28 2021 *)

Crossrefs

Sequence in context: A020432 A186471 A210305 * A032751 A020436 A104947

Adjacent sequences: A102745 A102746 A102747 * A102749 A102750 A102751

Keyword

nonn

Author

Pierre CAMI, Feb 09 2005

Extensions

More terms from Amiram Eldar, Aug 28 2021

Status

approved