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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

(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)}
(Magma) [n: n in [1..5*10^3] |IsPrime(n^3+n-1) and IsPrime(n^3 +n+1)]; // Vincenzo Librandi, Dec 26 2015
(PARI) isok(n) = isprime(n^3+n+1) && isprime(n^3+n-1); \\ Michel Marcus, Dec 27 2015

Crossrefs

Intersection of A049407 and A236475.

Sequence in context: A163785 A080793 A077225 * A039559 A045753 A022381

Adjacent sequences: A236523 A236524 A236525 * A236527 A236528 A236529

Keyword

nonn

Author

Derek Orr, Jan 27 2014

Status

approved