A238735 Number of prime pairs {2^n + (2k + 1), (2k + 1)*2^n + 1}, k < n.

1, 2, 1, 2, 0, 3, 2, 2, 0, 1, 0, 2, 0, 0, 0, 3, 0, 1, 0, 3, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 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 (which is either 2 or a Fermat prime; see A019434, A092506).

Examples

			a(1) = 1 because 2^1+(2*0+1)=3 and (2*0+1)*2^1+1=3 is prime pair for k=0,
a(2) = 2 because 2^2+(2*0+1)=5 and (2*0+1)*2^2+1=5 is prime pair for k=0, 2^2+(2*1+1)=7 and (2*1+1)*2^2+1=13 is prime pair for k=1,
a(3) = 1 because 2^3+(2*2+1)=13 and (2*2+1)*2^3+1=41 is prime pair for k=2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..631

Crossrefs

Cf. A019434, A238554.

Programs

Mathematica

a[n_] := Length@Select[Range[0, n-1], PrimeQ[2^n + (2*# + 1)] && PrimeQ[(2*# + 1)*2^n + 1] &]; Array[a, 100] (* Giovanni Resta, Mar 04 2014 *)

PARI

a(n)=sum(k=0,n-1,isprime(2^n+2*k+1)&&isprime((2*k+1)<Charles R Greathouse IV, Mar 06 2014

Extensions

a(47)-a(87) from Giovanni Resta, Mar 04 2014