A182253 Nonprime numbers n such that n^2 + n + 1 is prime.

1, 6, 8, 12, 14, 15, 20, 21, 24, 27, 33, 38, 50, 54, 57, 62, 66, 69, 75, 77, 78, 80, 90, 99, 105, 110, 111, 117, 119, 138, 141, 143, 147, 150, 153, 155, 161, 162, 164, 168, 176, 188, 189, 192, 194, 203, 206, 209, 215, 218, 231, 236, 245, 246, 266, 272, 278

Offset: 1

Author

Bernard Schott, Dec 18 2012

Keywords

• nonn

Comments

All these numbers are in A002384 but not in A053182.

The generated prime numbers n^2 + n + 1 are in A185632.

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

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.

Crossrefs

Cf. A002383, A002384, A053182, A053183, A085104, A125134, A185632.

Programs

Mathematica

Select[Range@ 280, And[! PrimeQ@ #, PrimeQ[#^2 + # + 1]] &] (* Michael De Vlieger, Jul 30 2017 *)

PARI

isok(n) = ! isprime(n) && isprime(n^2 + n + 1); \\ Michel Marcus, Sep 04 2013