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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

Table of n, a(n) for n=1..16.

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

Cf. A125083, A237527, A237528, A237639.

Sequence in context: A208397 A098129 A198603 * A258489 A015079 A015042

Adjacent sequences:  A237637 A237638 A237639 * A237641 A237642 A237643

KEYWORD

nonn

AUTHOR

Derek Orr, Feb 10 2014

STATUS

approved

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Last modified June 18 20:45 EDT 2021. Contains 345121 sequences. (Running on oeis4.)