A354829 Numbers k such that 2^k + 3^k + 6 is prime.

1, 2, 3, 4, 5, 8, 9, 15, 18, 23, 24, 33, 34, 35, 44, 63, 88, 89, 120, 220, 228, 229, 570, 1095, 1863, 2094, 2718, 3598, 4658, 6056, 8819, 9485, 11220, 23656, 28762, 35664, 36544, 39779, 46868, 50098, 58853

Offset: 1

Author

Hemjyoti Nath, Jun 07 2022

Keywords

• nonn
• more
• hard

Comments

a(34) > 17000.

a(36) > 30000. - Jon E. Schoenfield, Jun 14 2022

Examples

			For k=1 we obtain f(1) = 2^1 + 3^1 + 6 = 11 which is a prime.
		

Crossrefs

Cf. A353102.

Programs

Mathematica

Select[Range[1, 1000], PrimeQ[2^# + 3^# + 6] &]

Python

from sympy import isprime
from itertools import count, islice
def agen(): yield from (k for k in count(1) if isprime(2**k+3**k+6))
print(list(islice(agen(), 24))) # Michael S. Branicky, Jun 07 2022

Extensions

a(34) from Jon E. Schoenfield, Jun 11 2022

a(35) from Jon E. Schoenfield, Jun 13 2022

a(36)-a(38) from Michael S. Branicky, Mar 14 2023

a(39)-a(41) from Michael S. Branicky, Jun 01 2024