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

%I A236526 #30 Sep 08 2022 08:46:06
%S A236526 3,15,18,21,39,87,117,120,135,243,360,366,381,426,429,615,642,723,879,
%T A236526 1002,1023,1170,1173,1224,1458,1506,1518,1530,1731,1896,1920,1965,
%U A236526 2007,2025,2058,2133,2160,2376,2379,2382,2406,2553,2577,2673,2703,2727
%N A236526 Numbers k such that k^3 + k +- 1 are twin primes.
%C A236526 The only prime in this sequence is a(1) = 3.
%H A236526 Amiram Eldar, <a href="/A236526/b236526.txt">Table of n, a(n) for n = 1..10000</a>
%e A236526 381^3 + 381 +- 1 (55305961 and 55305959, respectively) are both prime. Thus, 381 is a member of this sequence.
%t A236526 Select[Range[3000], PrimeQ[#^3 + # - 1] && PrimeQ[#^3 + # + 1] &] (* _Vincenzo Librandi_, Dec 26 2015 *)
%t A236526 Select[Range[3000],AllTrue[#^3+#+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 23 2020 *)
%o A236526 (Python)
%o A236526 import sympy
%o A236526 from sympy import isprime
%o A236526 {print(n) for n in range(10**4) if isprime(n**3+n-1) and isprime(n**3+n+1)}
%o A236526 (Magma) [n: n in [1..5*10^3] |IsPrime(n^3+n-1) and IsPrime(n^3 +n+1)]; // _Vincenzo Librandi_, Dec 26 2015
%o A236526 (PARI) isok(n) = isprime(n^3+n+1) && isprime(n^3+n-1); \\ _Michel Marcus_, Dec 27 2015
%Y A236526 Intersection of A049407 and A236475.
%K A236526 nonn
%O A236526 1,1
%A A236526 _Derek Orr_, Jan 27 2014