A192515 Number of primes in the range [2^n-n^2, 2^n].

0, 1, 2, 4, 6, 8, 9, 10, 11, 15, 15, 16, 16, 18, 19, 20, 21, 23, 23, 31, 24, 34, 28, 27, 35, 32, 41, 38, 46, 45, 38, 44, 36, 49, 51, 43, 61, 33, 48, 58, 42, 62, 67, 59, 63, 70, 57, 63, 73, 68, 85, 74, 75, 73, 77, 86, 85, 74, 94, 89, 83, 89, 94, 93, 97, 102

Offset: 0

Author

Juri-Stepan Gerasimov, Jul 03 2011

Keywords

• nonn

Examples

			a(0)=0 because [2^0-0^2, 2^0]=[1, 1],
a(1)=1 because 2 in range [2^1-1^2, 2^1]=[1, 2],
a(2)=2 because 2, 3 in range [2^2-2^2, 2^2]=[0, 4],
a(3)=4 because 2, 3, 5, 7 in range [2^3-3^2, 2^3]=[-1, 8],
a(4)=6 because 2, 3, 5, 7, 11, 13 in range [2^4-4^2, 2^4]=[0, 16],
a(5)=8 because 7, 11, 13, 17, 19, 23, 29, 31 in range [2^5-5^2, 2^5]=[7, 32].
		

Crossrefs

Cf. A007053, A024012, A072180, A075896.

Programs

Maple

A192515 := proc(n) a := 0 ; for i from 2^n-n^2 to 2^n do if isprime(i) then a := a+1 ; end if; end do; a ; end proc: # R. J. Mathar, Jul 11 2011

Mathematica

Table[Count[Range[2^n - n^2, 2^n], p_ /; PrimeQ@ p], {n, 0, 65}] (* Michael De Vlieger, Apr 03 2016 *)

PARI

a(n) = primepi(2^n) - primepi(2^n-n^2) + isprime(2^n-n^2); \\ Michel Marcus, Apr 03 2016

Extensions

Corrected and extended by R. J. Mathar, Jul 11 2011