A237640 Numbers n of the form p^5 - Phi_5(p) (for prime p) such that n^5 - Phi_5(n) is also prime.

122, 340352, 830519696, 11479086422, 266390469692, 310503441398, 2718130415306, 14837993872846, 59538248604388, 889257663626476, 2496623039993996, 6427431330617746, 7120028814392596, 10777302002014868, 12942591289426088, 24039736320940828

Offset: 1

Author

Derek Orr, Feb 10 2014

Keywords

• nonn

Comments

All numbers are congruent to 2 mod 10, 6 mod 10, or 8 mod 10.

x^5 - Phi_5(x) = x^5-x^4-x^3-x^2-x-1.

Examples

			122 = 3^5-3^4-3^3-3^2-3^1-1 (3 is prime) and 122^5-122^4-122^3-122^2-122^1-1 = 26803717321 is prime. Thus, 122 is a member of this sequence.
		

Crossrefs

Cf. A125083, A237527, A237528, A237639.

Programs

Python

import sympy
from sympy import isprime
def poly5(x):
  if isprime(x):
    f = x**5-x**4-x**3-x**2-x-1
    if isprime(f**5-f**4-f**3-f**2-f-1):
      return True
  return False
x = 1
while x < 10**5:
  if poly5(x):
    print(x**5-x**4-x**3-x**2-x-1)
  x += 1