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

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, 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, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Mar 04 2014

Keywords

• nonn

Comments

If k = 0, then the two numbers in the "prime pair" are actually the same number, 2^n - 1 (a Mersenne prime; see A000668).

Examples

			a(2) = 1 because 2^2-(2*0+1)=3 and (2*0+1)*2^2-1=3 for k=0;
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;
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.
		

Crossrefs

Cf, A000043, A238694.

Programs

Mathematica

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 *)

Extensions

a(6), a(42), a(48)-a(87) from Giovanni Resta, Mar 04 2014