A240173 Numbers n such that k^n - 2^k is not prime for any k.

1, 2, 13, 43, 45, 51, 53, 55, 57, 63, 72, 77, 81, 84, 85, 89, 93, 103, 108, 117, 121, 129, 147, 149, 151, 163, 171, 173, 177, 183, 191, 213, 229, 231, 239, 241, 250, 259, 261, 263, 273, 283, 286, 291, 321, 331, 333, 344, 345, 351, 353, 361, 373, 381, 390, 399

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 02 2014

Keywords

• nonn

Comments

Numbers n such that A245459(n) = 0.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..64

Crossrefs

Cf. A245459.

Programs

Python

import sympy
def a(n):
  k = 2
  count = 0
  while k**n > 2**k:
    if sympy.isprime(k**n-2**k):
      count += 1
    k += 1
  return count
n = 1
while n < 1000:
  if not a(n):
    print(n, end=', ')
  n += 1 # Derek Orr, Aug 02 2014

Formula

A245459(a(n)) = 0.

Extensions

a(13)-a(34) from Derek Orr, Aug 02 2014

a(35) onwards from Amiram Eldar, Oct 03 2024