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A237422 Number of prime pairs {2^n - (2k + 1), (2k + 1)*2^n - 1}, k < n.

%I A237422 #23 Nov 07 2024 08:30:38
%S A237422 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 A237422 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 A237422 0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0
%N A237422 Number of prime pairs {2^n - (2k + 1), (2k + 1)*2^n - 1}, k < n.
%C A237422 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 A237422 a(2) = 1 because 2^2-(2*0+1)=3 and (2*0+1)*2^2-1=3 for k=0;
%e A237422 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 A237422 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 A237422 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 A237422 Cf, A000043, A238694.
%K A237422 nonn
%O A237422 1,3
%A A237422 _Ilya Lopatin_ and _Juri-Stepan Gerasimov_, Mar 04 2014
%E A237422 a(6), a(42), a(48)-a(87) from _Giovanni Resta_, Mar 04 2014