A381815 Smallest k>1 such that 10*k^(3*2^n)+1 is prime.

3, 2, 2, 2, 138, 24, 695, 107, 250, 404, 4657, 2185, 27931

Offset: 0

Author

Jakub Buczak, Mar 07 2025

Keywords

• nonn
• base
• more
• hard

Examples

			a(0) = 3, because 10*3^(3*2^0)+1 equals 271 which is prime.
a(1) = 2, because 10*2^(3*2^1)+1 equals 641 which is prime.
		

Crossrefs

Cf. A007283, A002254, A089319.

Cf. A381793.

Programs

Python

from sympy import isprime
from itertools import count
def a(n): return next(k for k in count(2) if isprime(k**(3*(2**n)) * 10 + 1))

Extensions

a(10)-a(11) from Michael S. Branicky, Mar 07 2025

a(12) from Georg Grasegger, Apr 15 2025