A365639 Numbers k such that k! + k^3 + 1 is prime.

0, 1, 2, 4, 6, 16, 28, 42

Offset: 1

Author

Darío Clavijo, Sep 14 2023

Keywords

• nonn
• hard
• more

Comments

If k is a term then k+1 is not composite (since k! + k^3 + 1 is divisible by k+1 for a composite k > 4). - Amiram Eldar, Sep 14 2023

Any further terms exceed 50000. - Lucas A. Brown, Mar 05 2024

Crossrefs

Cf. A000040, A000142, A000578, A001093, A038507, A073308, A080668.

Programs

Mathematica

Select[Range[0, 50], ! CompositeQ[# + 1] && PrimeQ[#! + #^3 + 1] &] (* Amiram Eldar, Sep 14 2023 *)

Python

from sympy import isprime, factorial
print([k for k in range(0, 43) if isprime((factorial(k)+ k**3 + 1))])