A193366 Primes of the form n^4 + n^3 + n^2 + n + 1 where n is nonprime.

5, 22621, 245411, 346201, 637421, 837931, 2625641, 3835261, 6377551, 15018571, 16007041, 21700501, 30397351, 35615581, 52822061, 78914411, 97039801, 147753211, 189004141, 195534851, 209102521, 223364311, 279086341, 324842131, 421106401, 445120421, 566124791, 693025471, 727832821, 745720141, 880331261, 943280801, 987082981, 1544755411, 1740422941

Offset: 1

Author

Jonathan Vos Post, Dec 20 2012

Keywords

• nonn
• easy

Comments

Note that there are no primes of the form n^3 + n^2 + n + 1 = (n+1)*(n^2+1) as irreducible components over Z.

From Bernard Schott, May 15 2017: (Start)

These are the primes associated with A286094.

A088548 = A190527 Union {This sequence}.

All the numbers of this sequence n^4 + n^3 + n^2 + n + 1 = 11111_n with n > 1 are Brazilian numbers, so belong to A125134 and A085104. (End)

Examples

			a(1) = 1^4 + 1^3 + 1^2 + 1 + 1 = 5.
a(2) = 12^4 + 12^3 + 12^2 + 12 + 1 = 22621.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Bernard Schott, Les nombres brésiliens, Reprinted from Quadrature, no. 76, avril-juin 2010, pages 30-38.

Crossrefs

Subsequence of A088548.

Cf. A000040, A018252, A185632, A192321.

Cf. A049409, A053699, A065509, A085104, A088548, A125134, A190527, A286094.

Programs

Maple

for n from 1 to 150 do p(n):= 1+n+n^2+n^3+n^4;
if tau(n)>2 and isprime(p(n)) then print(n,p(n)) else fi od: # Bernard Schott, May 15 2017

Mathematica

Select[Map[Total[#^Range[0, 4]] &, Select[Range@ 204, ! PrimeQ@ # &]], PrimeQ] (* Michael De Vlieger, May 15 2017 *)

PARI

print1(5);forcomposite(n=4,1e3,if(isprime(t=n^4+n^3+n^2+n+1),print1(", "t))) \\ Charles R Greathouse IV, Mar 25 2013

Formula

{n^4 + n^3 + n^2 + n + 1 where n is in A018252}.