%I #5 Mar 31 2012 10:23:47
%S 2,3,3,39,4,4,6,5,6,5,7,11,6,29,6,6,6,6,7,10,9,9,8,8,7,26,9,8,7,10,47,
%T 14,10,9,12,31,15,9,8,8,12,9,14,21,10,9,25,261,8,9,8,8,9,8,14,10,16,9,
%U 15,10,9,12,11,14,9,12,9,791,10,9,16,20,15,9,11,10,16,15,26,9,12,11,10
%N Smallest k such that 2^kprime(n) is prime.
%C Conjecture: sequence is defined for all n. First unproved n: 286 Prime(286)=1871, up to date, tested up to k=40959, none 2^kPrime(286) is prime.
%C Primo was used for testing large primes.
%H Lei Zhou, <a href="http://www.bme.emory.edu/~lzhou/prime/">Between 2^n and primes</a>.
%e Prime(1)=2, 2^22 = 2 is prime
%e Prime(2)=3, 2^33 = 5 is prime
%e ...
%e Prime(68)=337, 2^791337 is prime.
%t f[n_] := Block[{p = Prime@ n}, k = Ceiling@ Log2@ p; While[! PrimeQ[2^k  p], k++]; k]; Array[f, 83]
%Y Cf. A094076.
%K nonn
%O 1,1
%A _Lei Zhou_, Jan 20 2005
