A239321 Numbers n such that n - k! is never prime; or A175940(n) = 0.

1, 2, 10, 16, 22, 28, 34, 36, 40, 46, 50, 51, 52, 56, 57, 58, 64, 66, 70, 76, 78, 82, 86, 87, 88, 92, 93, 94, 96, 100, 101, 106, 112, 116, 117, 118, 120, 124, 126, 130, 134, 135, 136, 142, 144, 146, 147, 148, 154, 156, 160, 162, 166, 170, 171, 172, 176, 177

Offset: 1

Author

Derek Orr, Mar 15 2014

Keywords

• nonn

Examples

			51 - 0! = 51 - 1! = 50 is not prime. 51 - 2! = 49 is not prime. 51 - 3! = 45 is not prime. 51 - 4! = 27 is not prime. For k >= 5, 51 - k! is negative and thus not prime. Hence 51 is a member of this sequence since 51 - k! is not prime for any k.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A175940, A125163.

Programs

PARI

isok(n) = {k = 0; while (((nmk =(n - k!)) > 0), if (isprime(nmk), return (0)); k++;); return (1);} \\ Michel Marcus, Mar 16 2014

Python

import sympy
from sympy import isprime
import math
def Prf(x):
  count = 0
  for i in range(x):
    if isprime(x-math.factorial(i)):
      count += 1
  return count
x = 1
while x < 10**3:
  if Prf(x) == 0:
    print(x)
  x += 1