A357110 Numbers k such that 1 + k^2 * 2^k + k^3 * 3^k is prime.

2, 4, 6, 10, 12, 28, 30, 52, 60, 1170, 1292, 1882, 4760, 5160, 8388, 14652, 37700, 62388

Offset

1,1

Comments

a(17) > 52000.

a(18) > 10^5. - Michael S. Branicky, Aug 20 2025

Links

Table of n, a(n) for n=1..18.

Example

a(5) = 12 because 1 + 12^2 * 2^(12) + 12^3 * 3^(12) = 918919873 is prime.

Mathematica

p = 31000
ParallelTable[
If[PrimeQ[1 + n^2*2^n + n^3*3^n], n, Nothing], {n, 0, p}]

Prog

(PARI) is(n)=ispseudoprime(1 + n^2*2^n + n^3*3^n)
(Magma) [k: k in [1..31000] | IsPrime(1 + k^2*2^k + k^3*3^k)];
(Python)
from sympy import isprime
print([k for k in range(52000) if isprime(1 + (2**k)*(k**2) + (3**k)*(k**3))])

Crossrefs

Cf. A058780.

Sequence in context: A128169 A095923 A094960 * A100195 A032396 A271884

Adjacent sequences: A357107 A357108 A357109 * A357111 A357112 A357113

Keyword

nonn,more

Author

Enrico Masina, Sep 11 2022

Extensions

a(17) from Michael S. Branicky, Aug 20 2025

Status

approved