A152162 - OEIS

%I #7 Apr 01 2021 13:37:35

%S 0,1,1,2,2,3,3,4,4,5,7,6,16,9,9,8,9,10,9,10,10,14,15,13,15,15,16,15,

%T 24,17,17,21,23,17,18,45,26,25,22,23,24,21,36,25,34,23,40,35,32,42,25,

%U 26,30,32,33,31,33,32,31,30

%N Least k(n)>=floor(n/2) such that 3*2^k(n)*(2^n-1)-1 or 3*2^k(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 log(2)

%H Pierre CAMI, <a href="/A152162/b152162.txt">Table of n, a(n) for n = 1..2000</a>

%e 3*2^0*(2^1-1)-1=2 prime so k(1)=0 3*2^1*(2^2-1)-1=17 prime as 19 so k(2)=1 3*2^1*(2^3-1)-1=41 prime as 43 so k(2)=1

%t lk[n_]:=Module[{k=Floor[n/2],c=3(2^n-1)},While[NoneTrue[2^k*c+{1,-1},PrimeQ],k++];k]; Array[lk,60] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 01 2021 *)

%K nonn

%O 1,4

%A _Pierre CAMI_, Nov 27 2008