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%I #9 Jun 05 2015 18:57:25
%S 1,2,6,2,12,2,14,4,4,84,4,62,80,12,4,78,20,26,78,2,78,112,356,96,76,
%T 34,2,112,24,6,4,62,188,172,96,194,46,18,30,544,168,204,52,126,186,32,
%U 24,4,60,352,94,12,250,32,28,76,136,10,2794,4,46,16,178,58,886,104,74,54
%N Least number k such that (k+1)^prime(n) - (k-1)^prime(n) is a semiprime.
%C a(n) is even for n > 1.
%C (k+1)^M-(k-1)^M is divisible by 2 for any n. Thus, if it is a semiprime, then ((k+1)^M-(k-1)^M)/2 must be prime. This is only prime if M is also prime. Thus we may assume M is a prime.
%e (6+1)^(prime(3))-(6-1)^(prime(3)) = 7^5-5^5 = 13682 = 2*6841. Thus a(3) = 6.
%t lnk[n_]:=Module[{k=1},While[PrimeOmega[(k+1)^n-(k-1)^n]!=2,k++];k]; lnk/@Prime[Range[70]] (* _Harvey P. Dale_, Jun 05 2015 *)
%o (PARI) a(n)=for(k=1,10^4,if(ispseudoprime(((k+1)^prime(n)-(k-1)^prime(n))/2),return(k)))
%o n=1;while(n<100,print1(a(n),", ");n+=1)
%K nonn
%O 1,2
%A _Derek Orr_, Jun 01 2014
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