A236526 Numbers k such that k^3 + k +- 1 are twin primes.

3, 15, 18, 21, 39, 87, 117, 120, 135, 243, 360, 366, 381, 426, 429, 615, 642, 723, 879, 1002, 1023, 1170, 1173, 1224, 1458, 1506, 1518, 1530, 1731, 1896, 1920, 1965, 2007, 2025, 2058, 2133, 2160, 2376, 2379, 2382, 2406, 2553, 2577, 2673, 2703, 2727

Offset: 1

Author

Derek Orr, Jan 27 2014

Keywords

• nonn

Comments

The only prime in this sequence is a(1) = 3.

Examples

			381^3 + 381 +- 1 (55305961 and 55305959, respectively) are both prime. Thus, 381 is a member of this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A049407 and A236475.

Programs

Magma

[n: n in [1..5*10^3] |IsPrime(n^3+n-1) and IsPrime(n^3 +n+1)]; // Vincenzo Librandi, Dec 26 2015

Mathematica

Select[Range[3000], PrimeQ[#^3 + # - 1] && PrimeQ[#^3 + # + 1] &] (* Vincenzo Librandi, Dec 26 2015 *)
Select[Range[3000],AllTrue[#^3+#+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 23 2020 *)

PARI

isok(n) = isprime(n^3+n+1) && isprime(n^3+n-1); \\ Michel Marcus, Dec 27 2015

Python

import sympy
from sympy import isprime
{print(n) for n in range(10**4) if isprime(n**3+n-1) and isprime(n**3+n+1)}