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

0,3

Links

Table of n, a(n) for n=0..78.

Example

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].

Maple

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

Prog

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

Crossrefs

Sequence in context: A378304 A285110 A323018 * A225182 A014710 A055174

Adjacent sequences: A192061 A192062 A192063 * A192065 A192066 A192067

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 03 2011

Extensions

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

Status

approved