login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A095018 a(n) is the number of primes p which have exactly n zeros and n ones when written in binary. 10
1, 0, 2, 4, 17, 28, 189, 531, 1990, 5747, 23902, 76658, 291478, 982793, 3677580, 13214719, 49161612 (list; graph; refs; listen; history; text; internal format)
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..17.

A. Karttunen and 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)]

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 14 08:20 EDT 2020. Contains 336480 sequences. (Running on oeis4.)