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%I #10 Oct 31 2013 12:17:24
%S 1,1,1,2,3,7,11,21,37,67,125,227,431,787,1491,2812,5296,10055,19079,
%T 36343,69398,132661,254122,488028,937994,1806147,3482463,6722625,
%U 12994889,25145151,48709705,94451647,183312229,356089665,692285717
%N Number of primes whose binary expansion begins '11' (A080166) in range ]2^n,2^(n+1)].
%C I.e. number of primes p such that (2^n + 2^(n-1)) < p < 2^(n+1).
%C 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
%H A. Karttunen, J. Moyer: <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>
%H <a href="/index/Pri#primesubsetpop2">Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]</a>
%t f[n_] := PrimePi[2^(n + 1)] - PrimePi[2^n + 2^(n - 1) - 1]; Array[f, 35] (* _Robert G. Wilson v_ *)
%o (PARI) a(n)=primepi(2^(n+1))-primepi(2^n+2^(n-1)-1) \\ _Charles R Greathouse IV_, Sep 25 2012
%Y a(n) = A036378(n)-A095765(n).
%K nonn
%O 1,4
%A _Antti Karttunen_, Jun 12 2004
%E a(34) and a(35) from _Robert G. Wilson v_, Jan 24 2006