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%I #19 Mar 04 2014 23:53:07
%S 0,1,2,2,1,1,1,1,0,2,0,2,2,1,0,1,1,1,1,1,2,1,0,0,0,0,0,0,0,0,1,1,1,0,
%T 1,1,3,0,0,0,1,2,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,1,2,0,1,0,0,1,0,
%U 0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0
%N Number of prime pairs {2^n - (2k + 1), (2k + 1)*2^n - 1}, k < n.
%C If k = 0, then the two numbers in the "prime pair" are actually the same number, 2^n - 1 (a Mersenne prime; see A000668).
%e a(2) = 1 because 2^2-(2*0+1)=3 and (2*0+1)*2^2-1=3 for k=0;
%e a(3) = 2 because 2^3-(2*0+1)=7 and (2*0+1)*2^3-1=7 for k=0, 2^3-(2*1+1)=5 and (2*1+1)*2^3-1=23 for k=1;
%e a(4) = 2 because 2^4-(2*1+1)=13 and (2*1+1)*2^4-1)=47 for k=1, 2^4-(2*2+1)=11 and (2*2+1)*2^4-1=59 for k=2.
%t a[n_] := Length@Select[Range[0, n-1], PrimeQ[2^n - (2*#+1)] && PrimeQ[(2*#+1) * 2^n-1] &]; Array[a,90] (* _Giovanni Resta_, Mar 04 2014 *)
%Y Cf, A000043, A238694.
%K nonn
%O 1,3
%A _Ilya Lopatin_ and _Juri-Stepan Gerasimov_, Mar 04 2014
%E a(6), a(42), a(48)-a(87) from _Giovanni Resta_, Mar 04 2014
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