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a(n) = number of primes of the form 2^n - 3^k.
1

%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