A213790 Least number k such that 10^(n+k) - 10^n - 1 is prime.

1, 10, 1, 2, 2, 3, 1, 6, 2, 20, 3, 4, 30, 9, 4, 5, 14, 4, 1, 658, 6, 10, 32, 9, 2, 9, 109, 8, 1, 7, 12, 6, 4, 2, 5, 137, 1, 15, 112, 30, 237, 83, 12, 21, 5, 4, 20, 15, 42, 3, 16, 41, 26, 60, 157, 8, 16, 76, 69, 10, 4, 4, 120, 39, 8, 7, 115, 22, 14, 2, 102

Offset: 1

Author

Pierre CAMI, Jun 20 2012

Keywords

• nonn

Comments

Near repdigit primes: concatenation of k-1 9's, one 8, and n 9's.

Examples

			(10^1-1)*10^1-1 = 89 prime so a(1) = 1.
(10^10-1)*10^2-1 = 999999999899 prime so a(2) = 10.
		

Links

• Pierre CAMI, Table of n, a(n) for n = 1..1100

Programs

Mathematica

lnk[n_]:=Module[{k=1,c=10^n+1},While[!PrimeQ[10^(n+k)-c],k++];k]; Array[lnk,80] (* Harvey P. Dale, Aug 12 2024 *)

PARI

a(n) = {my(k=1); while (!ispseudoprime(10^(n+k) - 10^n - 1), k++); k;} \\ Michel Marcus, Sep 21 2019