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Numbers n such that n^4 + n +- 1 are twin primes.
2

%I #17 Sep 08 2022 08:46:06

%S 2,6,9,12,26,44,72,77,119,204,266,290,351,506,539,542,561,644,741,807,

%T 861,924,992,996,1016,1032,1049,1356,1412,1556,1640,1794,1847,1862,

%U 1871,1895,1980,2036,2129,2222,2289,2354,2445,2616,2630

%N Numbers n such that n^4 + n +- 1 are twin primes.

%H Harvey P. Dale, <a href="/A236760/b236760.txt">Table of n, a(n) for n = 1..1000</a>

%e 992^4 + 992 + 1 (968381957089) and 992^4 + 992 - 1 (968381957087) are twin primes. Thus, 992 is a member of this sequence.

%t Select[Range[3000], PrimeQ[#^4 + # - 1] && PrimeQ[#^4 + # + 1] &] (* _Vincenzo Librandi_, Dec 26 2015 *)

%t Select[Range[3000],AllTrue[#^4+#+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Oct 13 2017 *)

%o (Python)

%o import sympy

%o from sympy import isprime

%o {print(n) for n in range(10**4) if isprime(n**4+n-1) and isprime(n**4+n+1)}

%o (PARI)

%o s=[]; for(n=1, 3000, if(isprime(n^4+n+1)&&isprime(n^4+n-+1), s=concat(s, n))); s \\ _Colin Barker_, Jan 31 2014

%o (Magma) [n: n in [1..5*10^3] |IsPrime(n^4+n-1) and IsPrime(n^4 +n+1)]; // _Vincenzo Librandi_, Dec 26 2015

%Y Intersection of A236759 and A049408.

%K nonn,easy

%O 1,1

%A _Derek Orr_, Jan 30 2014