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Number of k such that (2^k-1)*2^n-1 is prime with 0 < k < n+1.
4

%I #20 Sep 16 2024 17:53:02

%S 0,2,2,2,4,1,3,1,2,2,5,1,4,2,1,2,4,3,3,1,2,1,4,1,1,1,0,2,3,1,6,1,3,1,

%T 2,3,3,3,3,1,7,3,2,1,4,2,3,1,3,1,2,2,3,1,4,3,3,1,3,0,4,0,3,3,3,2,1,2,

%U 0,3,1,2,4,4,3,1,4,2,3,3,3,2,3,6,0,4,4,2,3

%N Number of k such that (2^k-1)*2^n-1 is prime with 0 < k < n+1.

%C As n increases sum of a(n) from 1 to n / n tends to 2.66.

%H Pierre CAMI, <a href="/A197116/b197116.txt">Table of n, a(n) for n = 1..3000</a>

%t Table[Count[2^n (2^Range[n]-1)-1,_?PrimeQ],{n,90}] (* _Harvey P. Dale_, Sep 16 2024 *)

%o (PARI) a(n) = {nb = 0; for (k=1, n, if (isprime((2^k-1)*2^n-1), nb++);); return (nb);} \\ _Michel Marcus_, Mar 07 2013

%Y Cf. A197117, A197118, A197119.

%K nonn

%O 1,2

%A _Pierre CAMI_, Oct 11 2011