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A095765 Number of primes in range [2^n,2^(n+1)] whose binary expansion begins '10' (A080165). 3
0, 1, 1, 3, 4, 6, 12, 22, 38, 70, 130, 237, 441, 825, 1539, 2897, 5453, 10335, 19556, 37243, 70938, 135555, 259586, 497790, 956126, 1839597, 3544827, 6839282, 13212389, 25552386, 49472951, 95883938, 186011076, 361177503, 701906519 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

Ratio a(n)/A036378(n) converges as follows: 0, 0.5, 0.5, 0.6, 0.571429, 0.461538, 0.521739, 0.511628, 0.506667, 0.510949, 0.509804, 0.510776, 0.505734, 0.511787, 0.507921, 0.507444, 0.507303, 0.506866, 0.506173, 0.506115, 0.505487, 0.505395, 0.505318, 0.504951, 0.504786, 0.504588, 0.504437, 0.504301, 0.50415, 0.504016, 0.503887, 0.503763, 0.503654

Ratio a(n)/A095766(n) converges as follows: 0, 1, 1, 1.5, 1.333333, 0.857143, 1.090909, 1.047619, 1.027027, 1.044776, 1.04, 1.044053, 1.023202, 1.048285, 1.032193, 1.030228, 1.029645, 1.027847, 1.025001, 1.024764, 1.022191, 1.021815, 1.021501, 1.020003, 1.019331, 1.01852, 1.017908, 1.017353, 1.016737, 1.016195, 1.015669, 1.015164, 1.014723

I think this explains also the bias present in ratios shown at A095297, A095298, etc.

LINKS

Table of n, a(n) for n=1..35.

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)]

Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]

MATHEMATICA

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

CROSSREFS

a(n) = A036378(n)-A095766(n).

Sequence in context: A210523 A109069 A124571 * A095016 A160684 A176045

Adjacent sequences:  A095762 A095763 A095764 * A095766 A095767 A095768

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 12 2004

EXTENSIONS

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

STATUS

approved

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Last modified November 13 01:54 EST 2019. Contains 329085 sequences. (Running on oeis4.)