A095766 Number of primes whose binary expansion begins '11' (A080166) in range ]2^n,2^(n+1)].

1, 1, 1, 2, 3, 7, 11, 21, 37, 67, 125, 227, 431, 787, 1491, 2812, 5296, 10055, 19079, 36343, 69398, 132661, 254122, 488028, 937994, 1806147, 3482463, 6722625, 12994889, 25145151, 48709705, 94451647, 183312229, 356089665, 692285717

Offset: 1

Author

Antti Karttunen, Jun 12 2004

Keywords

• nonn

Comments

I.e. number of primes p such that (2^n + 2^(n-1)) < p < 2^(n+1).

Ratio a(n)/A036378(n) converges as follows: 1, 0.5, 0.5, 0.4, 0.428571, 0.538462, 0.478261, 0.488372, 0.493333, 0.489051, 0.490196, 0.489224, 0.494266, 0.488213, 0.492079, 0.492556, 0.492697, 0.493134, 0.493827, 0.493885, 0.494513, 0.494605, 0.494682, 0.495049, 0.495214, 0.495412, 0.495563, 0.495699, 0.49585, 0.495984, 0.496113, 0.496237, 0.496346

Links

• A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence
• Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]

Crossrefs

a(n) = A036378(n)-A095765(n).

Programs

Mathematica

f[n_] := PrimePi[2^(n + 1)] - PrimePi[2^n + 2^(n - 1) - 1]; Array[f, 35] (* Robert G. Wilson v *)

PARI

a(n)=primepi(2^(n+1))-primepi(2^n+2^(n-1)-1) \\ Charles R Greathouse IV, Sep 25 2012

Extensions

a(34) and a(35) from Robert G. Wilson v, Jan 24 2006