A089319 Smallest k > 1 such that k^n followed by digit 1 is a prime.

3, 2, 3, 3, 6, 2, 3, 6, 3, 11, 7, 2, 70, 2, 22, 18, 43, 3, 4, 649, 15, 3, 37, 2, 24, 13, 4, 8, 40, 77, 19, 22, 13, 24, 292, 48, 4, 2, 109, 792, 30, 4, 18, 5, 7, 90, 28, 138, 132, 891, 9, 25, 145, 2, 24, 9, 40, 28, 219, 165, 40, 41, 4, 13, 261, 24, 6, 30, 6, 154, 82, 22, 120, 2, 55

Offset: 1

Author

Amarnath Murthy, Nov 03 2003

Keywords

• base
• nonn

Examples

			a(4) = 3 as concatenation of 3^4 and 1 = 811 is a prime. 161 is not a prime.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A089318.

Programs

Mathematica

Do[k = 2; While[ !PrimeQ[10*k^n + 1], k++ ]; Print[k], {n, 1, 30}] (* Ryan Propper, Jul 08 2005 *)

PARI

a(n) = my(k=2); while (!isprime(10*k^n+1), k++); k; \\ Michel Marcus, Mar 07 2025

Extensions

Corrected and extended by Ryan Propper, Jul 08 2005

Further terms from David Wasserman, Sep 09 2005