A109137 Numbers k such that k * (10^k - 1) + 1 is prime.

2, 14, 42, 144, 200, 302, 7242, 8718, 10568, 24438, 41734

Offset: 1

Author

Jason Earls, Aug 18 2005

Keywords

• more
• nonn

Comments

Larger values certified with ECM. No more up to 6000.

Crossrefs

Cf. A110807.

Programs

PARI

is(n)=ispseudoprime(n*(10^n-1)+1) \\ Charles R Greathouse IV, Jun 13 2017

Python

from sympy import isprime
def afind(limit, startk=1):
    k, pow10 = startk, 10**startk
    for k in range(startk, limit+1):
        if isprime(k*(pow10 - 1) + 1): print(k, end=", ")
        k += 1
        pow10 *= 10
afind(500) # Michael S. Branicky, Aug 26 2021

Extensions

a(7)-a(8) from Ryan Propper, Sep 20 2006

a(9) from Michael S. Branicky, Aug 26 2021

a(10) from Michael S. Branicky, Apr 05 2023

a(11) from Michael S. Branicky, Oct 17 2024