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URL: https://oeis.org/A237639

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A237639
Numbers n = p^4-p^3-p^2-p-1 (for prime p) such that n^4-n^3-n^2-n-1 is prime.
5
41, 56133395601, 89362058601, 590884122501, 1275627652881, 2775672202617, 6212311361721, 7534036143501, 27344792789601, 61180709716101, 124857759197601, 206926840439901, 580608824590341, 603653936046501, 1442441423278281, 1864059458505657
OFFSET
1,1
COMMENTS
All numbers are congruent to 1 mod 10 or 7 mod 10.
41 is the only prime in the sequence, since one of p, n, and n^4-n^3-n^2-n-1 must be divisible by 3. - Charles R Greathouse IV, Feb 11 2014
EXAMPLE
41 = 3^4-3^3-3^2-3^1-1 (3 is prime) and 41^4-41^3-41^2-41^1-1 = 2755117 is prime. So, 41 is a member of this sequence.
PROG
(Python)
import sympy
from sympy import isprime
def poly4(x):
if isprime(x):
f = x**4-x**3-x**2-x-1
if isprime(f**4-f**3-f**2-f-1):
return True
return False
x = 1
while x < 10**5:
if poly4(x):
print(x**4-x**3-x**2-x-1)
x += 1
(PARI) s=[]; forprime(p=2, 7000, n=p^4-p^3-p^2-p-1; if(isprime(n^4-n^3-n^2-n-1), s=concat(s, n))); s \\ Colin Barker, Feb 11 2014
CROSSREFS
Cf. A125082.
Sequence in context: A228555 A297058 A125194 * A095189 A023932 A243831
KEYWORD
nonn
AUTHOR
Derek Orr, Feb 10 2014
STATUS
approved