A095070 One-bit dominant primes, i.e., primes whose binary expansion contains more 1's than 0's.

3, 5, 7, 11, 13, 19, 23, 29, 31, 43, 47, 53, 59, 61, 71, 79, 83, 89, 101, 103, 107, 109, 113, 127, 151, 157, 167, 173, 179, 181, 191, 199, 211, 223, 227, 229, 233, 239, 241, 251, 271, 283, 307, 311, 313, 317, 331, 347, 349, 359, 367, 373, 379, 383

Offset: 1

Author

Antti Karttunen, Jun 01 2004

Keywords

• nonn
• easy
• base

Examples

			23 is in the sequence because 23 is a prime and 23_10 = 10111_2. '10111' has four 1's and one 0. - _Indranil Ghosh_, Jan 31 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..20000
• Antti Karttunen and John Moyer, C-program for computing the initial terms of this sequence.
• MathOverflow, Primes with more ones than zeroes in their Binary expansion, 2012.

Crossrefs

Intersection of A000040 and A072600.

Complement of A095075 in A000040.

Subsequence: A095073.

Cf. A095020.

Programs

Mathematica

Select[Prime[Range[70]], Plus@@IntegerDigits[#, 2] > Length[IntegerDigits[#, 2]]/2 &] (* Alonso del Arte, Jan 11 2011 *)
Select[Prime[Range[100]], Differences[DigitCount[#, 2]][[1]] < 0 &] (* Amiram Eldar, Jul 25 2023 *)

PARI

B(x) = {nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
if(b1 > b0, return(1);, return(0););};
forprime(x = 3, 383, if(B(x), print1(x, ", "); ); ); \\ Washington Bomfim, Jan 11 2011

PARI

has(n)=hammingweight(n)>#binary(n)/2
select(has, primes(500)) \\ Charles R Greathouse IV, May 02 2013

Python

# Program to generate the b-file
from sympy import isprime
i=1
j=1
while j<=200:
    if isprime(i) and bin(i)[2:].count("1")>bin(i)[2:].count("0"):
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Jan 31 2017