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Least k such that 4^n - 2^k - 1 is prime with n-1 < k < 2*n or 0 if no solution.
1

%I #12 May 02 2012 12:54:08

%S 0,2,4,4,5,7,8,11,9,10,16,13,0,23,16,23,28,18,20,23,22,30,0,29,26,47,

%T 28,42,0,33,41,0,42,48,37,45,53,38,57,46,0,70,66,52,45,0,49,81,58,50,

%U 74,86,0,57,56,94,57,0,64,80,96,64,72,97,77,87,0,104,77

%N Least k such that 4^n - 2^k - 1 is prime with n-1 < k < 2*n or 0 if no solution.

%C Less than 10 % of a(n)=0.

%H Pierre CAMI, <a href="/A182414/b182414.txt">Table of n, a(n) for n = 1..4560</a>

%e n=2:2^(2*n)-2^1-1=13 prime but n-1=1=k so k not > n-1.

%e 2^(2*n)-2^2-1=11 prime k=2 k>n-1 so a(2)=2.

%t Table[k = n; While[k < 2*n && ! PrimeQ[4^n - 2^k - 1], k++]; If[k == 2*n, k = 0]; k, {n, 100}] (* _T. D. Noe_, May 02 2012 *)

%Y Cf. A182413.

%K nonn

%O 1,2

%A _Pierre CAMI_, Apr 28 2012