

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
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OFFSET

1,1


COMMENTS

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


LINKS



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+n1) and isprime(n**3+n+1)}
(Magma) [n: n in [1..5*10^3] IsPrime(n^3+n1) and IsPrime(n^3 +n+1)]; // Vincenzo Librandi, Dec 26 2015
(PARI) isok(n) = isprime(n^3+n+1) && isprime(n^3+n1); \\ Michel Marcus, Dec 27 2015


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



