cp's OEIS Frontend

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

%I A192515 #18 Apr 03 2016 10:24:52
%S A192515 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,
%T A192515 32,41,38,46,45,38,44,36,49,51,43,61,33,48,58,42,62,67,59,63,70,57,63,
%U A192515 73,68,85,74,75,73,77,86,85,74,94,89,83,89,94,93,97,102
%N A192515 Number of primes in the range [2^n-n^2, 2^n].
%e A192515 a(0)=0 because [2^0-0^2, 2^0]=[1, 1],
%e A192515 a(1)=1 because 2 in range [2^1-1^2, 2^1]=[1, 2],
%e A192515 a(2)=2 because 2, 3 in range [2^2-2^2, 2^2]=[0, 4],
%e A192515 a(3)=4 because 2, 3, 5, 7 in range [2^3-3^2, 2^3]=[-1, 8],
%e A192515 a(4)=6 because 2, 3, 5, 7, 11, 13 in range [2^4-4^2, 2^4]=[0, 16],
%e A192515 a(5)=8 because 7, 11, 13, 17, 19, 23, 29, 31 in range [2^5-5^2, 2^5]=[7, 32].
%p A192515 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
%t A192515 Table[Count[Range[2^n - n^2, 2^n], p_ /; PrimeQ@ p], {n, 0, 65}] (* _Michael De Vlieger_, Apr 03 2016 *)
%o A192515 (PARI) a(n) = primepi(2^n) - primepi(2^n-n^2) + isprime(2^n-n^2); \\ _Michel Marcus_, Apr 03 2016
%Y A192515 Cf. A007053, A024012, A072180, A075896.
%K A192515 nonn
%O A192515 0,3
%A A192515 _Juri-Stepan Gerasimov_, Jul 03 2011
%E A192515 Corrected and extended by _R. J. Mathar_, Jul 11 2011