A185632 Primes of the form n^2 + n + 1 where n is nonprime.

3, 43, 73, 157, 211, 241, 421, 463, 601, 757, 1123, 1483, 2551, 2971, 3307, 3907, 4423, 4831, 5701, 6007, 6163, 6481, 8191, 9901, 11131, 12211, 12433, 13807, 14281, 19183, 20023, 20593, 21757, 22651, 23563, 24181, 26083, 26407, 27061, 28393, 31153, 35533

Offset: 1

Author

Bernard Schott, Dec 18 2012

Keywords

• nonn

Comments

These are the primes associated with A182253.

All these numbers are in A002383 but not in A053183.

All the numbers n^2 + n + 1 = 111_n with n >= 2 are by definition Brazilian numbers: A125134. See Links: "Les nombres brésiliens" - Section V.5 page 35.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38.
• Bernard Schott, Les nombres brésiliens, Reprinted from Quadrature, no. 76, avril-juin 2010, pages 30-38, included here with permission from the editors of Quadrature.

Crossrefs

Cf. A002383, A002384, A053182, A053183, A182253.

Cf. A085104, A125134.

Programs

Mathematica

Select[Table[If[PrimeQ[n],Nothing,n^2+n+1],{n,200}],PrimeQ] (* Harvey P. Dale, Apr 02 2023 *)

PARI

lista(nn) = {for (n = 1, nn, if (! isprime(n) && isprime(p = n^2 + n + 1), print1(p, ", ");););} \\ Michel Marcus, Sep 04 2013