A286094 -id:A286094 - cp's OEIS frontend

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

Jonathan Vos Post, Dec 20 2012

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)

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

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.

Subsequence of A088548.
Cf. A000040, A018252, A185632, A192321.
Cf. A049409, A053699, A065509, A085104, A088548, A125134, A190527, A286094.

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

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

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

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

A308238 Nonprimes k such that k^10 + k^9 + k^8 + k^7 + k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 is prime.

Original entry on oeis.org

1, 20, 21, 30, 60, 86, 172, 195, 212, 224, 258, 268, 272, 319, 339, 355, 365, 366, 390, 398, 414, 480, 504, 534, 539, 543, 567, 592, 626, 654, 735, 756, 766, 770, 778, 806, 812, 874, 943, 973, 1003, 1036, 1040, 1065, 1194, 1210, 1239, 1243, 1264, 1309, 1311

Offset: 1

Bernard Schott, May 16 2019

nonn

A240693 Union {this sequence} = A162862.

The corresponding prime numbers, (11111111111)_k, are Brazilian primes and belong to A085104 and A285017 (except 11).

			(11111111111)_20 = (20^11 - 1)/19 = 10778947368421 is prime, thus 20 is a term.

Cf. A162861, A162862, A240693, A286301.
Intersection of A064108 and A285017.
Similar to A182253 for k^2+k+1, A286094 for k^4+k^3+k^2+k+1, A288939 for k^6+k^5+k^4+k^3+k^2+k+1.

[1] cat [n:n in [2..1500]|not IsPrime(n) and IsPrime(Floor((n^11-1)/(n-1)))]; // Marius A. Burtea, May 16 2019

filter:= n -> not isprime(n) and isprime((n^11-1)/(n-1)) : select(filter, [$2..5000]);

Select[Range@ 1320, And[! PrimeQ@ #, PrimeQ@ Total[#^Range[0, 10]]] &] (* Michael De Vlieger, Jun 09 2019 *)

isok(n) = !isprime(n) && isprime(polcyclo(11, n)); \\ Michel Marcus, May 19 2019

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula