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A152414 Least k(n) such that k(n)*2^n*(2^n-1)-1 or k(n)*2^n*(2^n-1)+1 is prime or both primes. 8

%I #8 Mar 07 2013 02:55:13

%S 1,1,2,1,1,3,3,6,1,1,4,2,5,3,9,8,4,1,3,4,36,5,2,4,10,4,18,3,21,9,6,1,

%T 6,8,12,2,51,1,2,2,21,6,6,12,1,5,5,3,10,1,11,53,9,4,3,2,1,5,12,10,9,8,

%U 5,9,7,6,62,29,16,51,12,3,30,56,2,23,70,3,23

%N Least k(n) such that k(n)*2^n*(2^n-1)-1 or k(n)*2^n*(2^n-1)+1 is prime or both primes.

%C As n increases, sum k(n) for i=1 to n / sum n for i=1 to n tends to 1/4. All values in b152414 verified and primes certified using PFGW from Primeform group.

%C Contribution from _Pierre CAMI_, Dec 04 2008: (Start)

%C for n even sum k(2*n) for i=1 to n / sum 2*n for i=1 to n tends to log(2)/4.

%C for n odd sum k(2*n+1) for i=0 to n / sum 2*n+1 for i=1 to n tends to 1/2-log(2)/4.

%C (End)

%H Pierre CAMI, <a href="/A152414/b152414.txt">Table of n, a(n) for n=1..4000</a>

%e 1*2^1*(2^1-1)+1=3 is prime so k(1)=1.

%e 1*2^2*(2^2-1)-1=11 is prime, as well as 13, so k(2)=1.

%e 2*2^3*(2^3-1)+1=113 is prime so k(3)=2.

%o (PARI) a(n) = {k = 1; while (! (isprime(k*2^n*(2^n-1)+1) || isprime(k*2^n*(2^n-1)-1)), k++); return (k);} \\ _Michel Marcus_, Mar 07 2013

%K nonn

%O 1,3

%A _Pierre CAMI_, Dec 03 2008

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