A173179 -id:A173179 - cp's OEIS frontend

A173180 Numbers k such that k^5-k^4-k^3-k^2-k-1 is prime.

4, 6, 8, 14, 18, 20, 24, 26, 28, 32, 40, 42, 50, 58, 62, 68, 72, 100, 104, 120, 122, 140, 150, 174, 184, 192, 210, 234, 240, 260, 266, 278, 288, 300, 306, 326, 346, 366, 404, 432, 444, 460, 464, 466, 470, 484, 488, 512, 516, 526, 538, 556, 562, 564, 570, 584

Offset: 1

Vladimir Joseph Stephan Orlovsky, Feb 11 2010

nonn

All terms are even. - Robert Israel, Apr 11 2019

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A002328, A008864, A162294, A173179

filter:= k -> isprime( k^5-k^4-k^3-k^2-k-1):
select(filter, 2*[$1..500]); # Robert Israel, Apr 11 2019

f[n_]:=n^5-n^4-n^3-n^2-n-1;Select[Range[7! ],PrimeQ[f[ #1]]&]
Select[Range[2,600,2],PrimeQ[#^5-Total[#^Range[0,4]]]&] (* Harvey P. Dale, Sep 26 2023 *)

{k: A125083(k) in A000040}. [R. J. Mathar, Feb 13 2010]

A240084 Primes p such that p^4-p^3-p^2-p-1 is prime.

Original entry on oeis.org

3, 11, 17, 41, 59, 71, 101, 113, 179, 233, 293, 347, 389, 449, 461, 503, 521, 617, 641, 683, 797, 953, 1319, 1439, 1487, 1493, 1823, 1877, 1973, 2087, 2339, 2351, 2633, 2663, 2789, 2801, 2909, 2927, 2957, 2963, 2999, 3011, 3167, 3467, 3527, 3677, 3851, 3881, 3923

Offset: 1

Derek Orr, Mar 31 2014

nonn

			3^4-3^3-3^2-3-1 = 41 is prime. Thus, 3 is a member of this sequence.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A173179.

Select[Prime[Range[600]],PrimeQ[#^4-#^3-#^2-#-1]&] (* Harvey P. Dale, Nov 23 2024 *)

s=[]; forprime(p=2, 4000, if(isprime(p^4-p^3-p^2-p-1), s=concat(s, p))); s \\ Colin Barker, Apr 01 2014

import sympy
from sympy import isprime
{print(p) for p in range(10**4) if isprime(p**4-p**3-p**2-p-1) and isprime(p)}

cp's OEIS Frontend

A173180 Numbers k such that k^5-k^4-k^3-k^2-k-1 is prime.

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