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A237640 Numbers n of the form p^5 - Phi_5(p) (for prime p) such that n^5 - Phi_5(n) is also prime. 1
122, 340352, 830519696, 11479086422, 266390469692, 310503441398, 2718130415306, 14837993872846, 59538248604388, 889257663626476, 2496623039993996, 6427431330617746, 7120028814392596, 10777302002014868, 12942591289426088, 24039736320940828 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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.
LINKS
EXAMPLE
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.
PROG
(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
CROSSREFS
Sequence in context: A208397 A098129 A198603 * A258489 A015079 A015042
KEYWORD
nonn
AUTHOR
Derek Orr, Feb 10 2014
STATUS
approved

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Last modified March 28 11:46 EDT 2024. Contains 371241 sequences. (Running on oeis4.)