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A236526 Numbers k such that k^3 + k +- 1 are twin primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 21 21:32 EDT 2021. Contains 347605 sequences. (Running on oeis4.)