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Least number k such that k^n - k +/- 1 are twin primes, or 0 if no such k exists.
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%I #7 Oct 04 2014 18:11:53

%S 3,2,6,2,4,30,0,27,4,9,109,14,0,70,58,208,12,65,0,172,1579,1639,585,

%T 208,0,494,505,79,3630,95,0,81,4422,130,1648,3,0,13030,174,3,627,9524,

%U 0,3858,1369,1235,11340,6411,0,35494,2553,4883,412,44366,0,14640,101386,44021,3003,13045

%N Least number k such that k^n - k +/- 1 are twin primes, or 0 if no such k exists.

%C For n > 2, if n == 2 (mod 6), then k^n - k + 1 is divisible by k^2 - k + 1. Thus it will never be prime.

%o (PARI)

%o a(n)=if(n>2&&n==Mod(2,6),return(0));k=1;while(!ispseudoprime(k^n-k+1)||!ispseudoprime(k^n-k-1),k++);k

%o n=2;while(n<100,print1(a(n),", ");n++)

%Y Cf. A131530, A236524, A236763.

%K nonn

%O 2,1

%A _Derek Orr_, Sep 30 2014