Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Oct 18 2017 14:19:51
%S 0,1,2,2,4,2,3,2,4,2,2,2,3,3,1,2,4,0,3,4,4,3,3,3,0,1,1,0,2,1,1,1,3,2,
%T 3,2,2,0,1,2,2,3,0,0,4,4,3,2,5,4,4,0,0,0,1,1,4,5,2,4,3,3,0,1,1,2,5,0,
%U 1,1,4,3,1,0,1,1,3,2,3,0,2,4,2,1,2,2,3,0,7,2,4,4,2,2,2,3,5,0,3,1,1,1,3,3,2
%N a(n) = number of primes of the form 2^n - 3^k.
%C a(1) = 0 because there are no prime numbers of the form 2^1 - 3^k. a(2) = 1 because the only prime of the form 2^2 - 3^k is 2^2 - 3^0 = 3. a(3) = because there are two primes of the form 2^3 - 3^k: 2^3 - 3^0 = 7 and 2^3 - 3^1 = 5.
%H G. C. Greubel, <a href="/A123674/b123674.txt">Table of n, a(n) for n = 1..1000</a>
%t Table[Length[Select[Range[0,Floor[Log[3,2^n]]],PrimeQ[2^n-3^# ]&]],{n,1,200}]
%K nonn
%O 1,3
%A _Alexander Adamchuk_, Nov 17 2006