A095018 a(n) is the number of primes p which have exactly n zeros and n ones when written in binary.

1, 0, 2, 4, 17, 28, 189, 531, 1990, 5747, 23902, 76658, 291478, 982793, 3677580, 13214719, 49161612, 177190667, 664806798, 2443387945

Offset

1,3

Comments

a(n) is the number of terms in A066196 which lie between 2^(2n-1) and 2^2n inclusively.

Links

Table of n, a(n) for n=1..20.

Antti Karttunen and John 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)]

Example

a(1) = 1 since only 2_10 = 10_2 satisfies the criterion;
a(2) = 0 since there is no prime between 4 and 16 which meets the criterion.
The only primes in the range ]2^5,2^6[ with equal numbers of ones and zeros in their binary expansion are 37 (in binary 100101) and 41 (in binary 101011) thus a(3)=2.
a(4) = 4 since 139, 149, 163 and 197 meet the criterion; etc.

Mathematica

f[n_] := Block[{c = 0, p = NextPrime[2^(2n -1) -1], lmt = 2^(2n)}, While[p < lmt, If[DigitCount[p, 2, 1] == n, c++]; p = NextPrime@ p]; c]; Array[f, 17] (* K. D. Bajpai and Robert G. Wilson v, Jan 10 2017 *)

Crossrefs

Cf. A066196, A095005, A095006, A095052, A095053, A280872.

Sequence in context: A318367 A317488 A103051 * A081356 A018269 A270359

Adjacent sequences: A095015 A095016 A095017 * A095019 A095020 A095021

Keyword

nonn,base

Author

Antti Karttunen, Jun 01 2004

Extensions

Edited by N. J. A. Sloane, Jan 16 2017

a(18)-a(20) from Amiram Eldar, Nov 21 2020

Status

approved