A191699 Numbers k such that k*(k-1)^k - (k-1)*k^(k-1) - 1 is prime.

3, 4, 6, 9, 31, 187, 632, 2972

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 12 2011

Keywords

• nonn
• hard
• more

Comments

a(9) > 20000. - Michael S. Branicky, Apr 13 2025

Examples

			a(1)=3 because 3*2^3-2*3^2-1=5 is prime, a(2)=4 because 4*3^4-3*4^3-1=131 is prime, a(3)=6 because 6*5^6-5*6^5-1=54869 is prime, a(4)=9 because 9*8^9-8*9^8-1=863585783 is prime.
		

Crossrefs

Cf. A191409 (associated primes).

Programs

Python

from sympy import isprime
def afind(limit, startk=1):
    for k in range(startk, limit+1):
        if isprime(k*(k-1)**k - (k-1)*k**(k-1) - 1):
            print(k, end=", ")
afind(200) # Michael S. Branicky, Jan 10 2022

Extensions

a(8) from Michael S. Branicky, Jan 10 2022