The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A088548

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A088548

Primes of the form k^4 + k^3 + k^2 + k + 1.
(history; published version)

#27 by Charles R Greathouse IV at Thu Sep 08 08:45:12 EDT 2022

PROG

(MAGMAMagma) [a: n in [0..200] | IsPrime(a) where a is n^4+n^3+n^2+n+1]; // Vincenzo Librandi, Jul 16 2012

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#26 by Michel Marcus at Mon May 31 10:56:23 EDT 2021

STATUS

reviewed

approved

#25 by Joerg Arndt at Mon May 31 09:11:22 EDT 2021

STATUS

proposed

reviewed

#24 by Michael S. Branicky at Mon May 31 09:07:49 EDT 2021

STATUS

editing

proposed

#23 by Michael S. Branicky at Mon May 31 08:56:36 EDT 2021

NAME

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

DATA

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

PROG

(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

STATUS

approved

editing

#22 by Alois P. Heinz at Sun Jul 30 16:49:39 EDT 2017

STATUS

reviewed

approved

#21 by Michel Marcus at Sun Jul 30 14:42:47 EDT 2017

STATUS

proposed

reviewed

#20 by Jon E. Schoenfield at Sun Jul 30 13:59:44 EDT 2017

STATUS

editing

proposed

#19 by Jon E. Schoenfield at Sun Jul 30 13:59:40 EDT 2017

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

EXAMPLE

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

CROSSREFS

Cf. A085104, A049409, A002383, A049409, A085104, A088550.

STATUS

approved

editing

#18 by R. J. Mathar at Fri Feb 07 06:07:12 EST 2014

STATUS

editing

approved