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

1,1

Links

Table of n, a(n) for n=1..8.

Example

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.

Prog

(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

Crossrefs

Cf. A191409 (associated primes).

Sequence in context: A102934 A338061 A350741 * A293272 A192286 A242028

Adjacent sequences: A191696 A191697 A191698 * A191700 A191701 A191702

Keyword

nonn,hard

Author

Juri-Stepan Gerasimov, Jun 12 2011

Extensions

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

Status

approved