A192064 Number of primes in the range [2^n-n, 2^n].

0, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 0, 1, 3, 3, 2, 3, 3, 2, 2, 2, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 1, 3, 2, 0, 2, 0, 2, 3, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 0, 2, 1, 3, 3, 2, 1, 0, 3, 1, 1, 1, 1, 2, 5, 1, 1, 1, 0, 0, 1, 3, 0, 2, 2, 1

Offset: 0

Author

Juri-Stepan Gerasimov, Jul 03 2011

Keywords

• nonn

Examples

			a(0)=0 because [2^0-0, 2^0]=[1, 1],
a(1)=1 because 2 in range [2^1-1, 2^1]=[1,2],
a(2)=2 because 2, 3 in range [2^2-2, 2^2]=[2, 4],
a(3)=2 because 5, 7 in range [2^3-3, 2^3]=[5, 8],
a(4)=1 because 13 in range [2^4-4, 2^4]=[12, 16],
a(5)=2 because 29, 31 in range [2^5-5, 2^5]=[27, 32].
		

Programs

Maple

A192064 := proc(n) numtheory[pi](2^n)-numtheory[pi](2^n-n-1) ; end proc: # R. J. Mathar, Jul 07 2011

PARI

a(n)=sum(k=2^n-n,2^n,isprime(k)) \\ Charles R Greathouse IV, Jul 03 2011

Extensions

Corrected and extended by Charles R Greathouse IV, Jul 03 2011