A389195 Numbers k such that k^k + (k+1)^(k-1) is prime.

0, 1, 2, 3, 5, 6, 7, 59, 87

Offset

1,3

Comments

a(10) > 10^4 if it exists. - Michael S. Branicky, Sep 25 2025

a(10) > 12600. - Brenden W. Lamp, Feb 02 2026

a(10) > 25000. - Michael S. Branicky, Feb 05 2026

Links

Table of n, a(n) for n=1..9.

Example

5 is a term because 5^5 + 6^4 = 4421, which is prime.

Prog

(Python)
from sympy import isprime
def ok(n): return n == 0 or isprime(n**n + (n+1)**(n-1))
print([k for k in range(100) if ok(k)])
(PARI) isok(k) = ispseudoprime(k^k + (k+1)^(k-1)); \\ Michel Marcus, Sep 25 2025

Crossrefs

Sequence in context: A343742 A357263 A067077 * A370688 A357132 A067183

Adjacent sequences: A389192 A389193 A389194 * A389196 A389197 A389198

Keyword

nonn,more,hard

Author

Brenden W. Lamp, Sep 25 2025

Status

approved