A088548 Primes of the form k^4 + k^3 + k^2 + k + 1.

5, 31, 2801, 22621, 30941, 88741, 245411, 292561, 346201, 637421, 732541, 837931, 2625641, 3500201, 3835261, 6377551, 15018571, 16007041, 21700501, 28792661, 30397351, 35615581, 39449441, 48037081, 52822061, 78914411, 97039801, 147753211, 189004141, 195534851

Offset

1,1

Comments

These numbers when >= 31 are primes repunits 11111_n in a base n >= 2, so except 5, they are all Brazilian primes belonging to A085104. (See Links "Les nombres brésiliens", § V.4 - § V.5.) A008858 is generated by the bases n present in A049409. - Bernard Schott, Dec 19 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.

Formula

A000040 intersect A053699. - R. J. Mathar, Feb 07 2014

Example

a(2) = 31 is prime and 31 = 2^4 + 2^3 + 2^2 + 2 + 1.

Mathematica

lst={}; Do[a=1+n+n^2+n^3+n^4; If[PrimeQ[a], AppendTo[lst, a]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jun 02 2009 *)
Select[Table[n^4+n^3+n^2+n+1, {n, 0, 2000}], PrimeQ] (* Vincenzo Librandi, Jul 16 2012 *)

Prog

(PARI) polypn(n, p) = { for(x=1, n, if(p%2, y=2, y=1); for(m=1, p, y=y+x^m; ); if(isprime(y), print1(y", ")); ) }
(Magma) [a: n in [0..200] | IsPrime(a) where a is n^4+n^3+n^2+n+1]; // Vincenzo Librandi, Jul 16 2012
(Python)
from sympy import isprime
print(list(filter(isprime, (k**4+k**3+k**2+k+1 for k in range(120))))) # Michael S. Branicky, May 31 2021

Crossrefs

Cf. A002383, A049409, A085104, A088550.

Sequence in context: A059301 A225158 A299887 * A244622 A278574 A062631

Adjacent sequences: A088545 A088546 A088547 * A088549 A088550 A088551

Keyword

nonn,easy

Author

Cino Hilliard, Nov 17 2003

Status

approved