A357110 - OEIS

%I #39 Aug 21 2025 02:43:16

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

%T 62388

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

%C a(17) > 52000.

%C a(18) > 10^5. - _Michael S. Branicky_, Aug 20 2025

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

%t p = 31000

%t ParallelTable[

%t If[PrimeQ[1 + n^2*2^n + n^3*3^n], n, Nothing], {n, 0, p}]

%o (PARI) is(n)=ispseudoprime(1 + n^2*2^n + n^3*3^n)

%o (Magma) [k: k in [1..31000] | IsPrime(1 + k^2*2^k + k^3*3^k)];

%o (Python)

%o from sympy import isprime

%o print([k for k in range(52000) if isprime(1 + (2**k)*(k**2) + (3**k)*(k**3))])

%Y Cf. A058780.

%K nonn,more

%O 1,1

%A _Enrico Masina_, Sep 11 2022

%E a(17) from _Michael S. Branicky_, Aug 20 2025