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

%I #24 Feb 13 2015 00:27:01

%S 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,

%T 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,

%U 1,1,1,0,0,1,3,0,2,2,1

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

%e a(0)=0 because [2^0-0, 2^0]=[1, 1],

%e a(1)=1 because 2 in range [2^1-1, 2^1]=[1,2],

%e a(2)=2 because 2, 3 in range [2^2-2, 2^2]=[2, 4],

%e a(3)=2 because 5, 7 in range [2^3-3, 2^3]=[5, 8],

%e a(4)=1 because 13 in range [2^4-4, 2^4]=[12, 16],

%e a(5)=2 because 29, 31 in range [2^5-5, 2^5]=[27, 32].

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

%o (PARI) a(n)=sum(k=2^n-n,2^n,isprime(k)) \\ _Charles R Greathouse IV_, Jul 03 2011

%K nonn

%O 0,3

%A _Juri-Stepan Gerasimov_, Jul 03 2011

%E Corrected and extended by _Charles R Greathouse IV_, Jul 03 2011

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Last modified April 24 19:52 EDT 2024. Contains 371963 sequences. (Running on oeis4.)