1,4

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.

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)]

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

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

Sequence in context: A111159 A109069 A124571 this_sequence A095016 A160684 A137333

Adjacent sequences: A095762 A095763 A095764 this_sequence A095766 A095767 A095768

nonn

Antti Karttunen (his-firstname.his-surname(AT)iki.fi), Jun 12 2004

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