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
Examples
a(5) = 12 because 1 + 12^2 * 2^(12) + 12^3 * 3^(12) = 918919873 is prime.
Crossrefs
Cf. A058780.
Programs
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Magma
[k: k in [1..31000] | IsPrime(1 + k^2*2^k + k^3*3^k)];
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Mathematica
p = 31000 ParallelTable[ If[PrimeQ[1 + n^2*2^n + n^3*3^n], n, Nothing], {n, 0, p}] -
PARI
is(n)=ispseudoprime(1 + n^2*2^n + n^3*3^n)
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Python
from sympy import isprime print([k for k in range(52000) if isprime(1 + (2**k)*(k**2) + (3**k)*(k**3))])
Extensions
a(17) from Michael S. Branicky, Aug 20 2025
Comments