A240083 Numbers n such that k^n-(k-1)^n-...-3^n-2^n is prime for some k.

1, 2, 3, 4, 5, 10, 11, 13, 15, 16, 17, 18, 19, 21, 22, 24, 26, 27, 28, 29, 31, 32, 33, 35, 41, 45, 46, 47, 48, 49, 53, 55, 57, 58, 59, 61, 65, 67, 71, 76, 82, 83, 87, 88, 89, 91, 93, 94, 99, 101, 103, 107, 108, 110, 111, 114, 115, 116, 119, 123, 127, 130, 132, 134, 138, 141

Offset: 1

Author

Derek Orr, Mar 31 2014

Keywords

• nonn

Comments

Also numbers n such that A239472(n) > 0.

Crossrefs

Cf. A239472.

Programs

PARI

a(n)=k=1;while((s=k^n-sum(i=2,k-1,i^n))>0,if(isprime(s),return(k));k++)
for(n=1,100,if(a(n),print1(n,", "))) \\ Derek Orr, Mar 12 2015

Python

import sympy
from sympy import isprime
def Lep(n):
  for k in range(2*10**3):
    num = k**n
    for i in range(2, k):
      num -= i**n
      if num < 0:
        return None
    if isprime(num):
      return k
n = 1
while n < 10**3:
  if Lep(n) != None:
    print(n)
  n += 1