A095071 Zero-bit dominant primes, i.e., primes whose binary expansion contains more 0's than 1's.

17, 67, 73, 97, 131, 137, 193, 257, 263, 269, 277, 281, 293, 337, 353, 389, 401, 449, 521, 523, 547, 577, 593, 641, 643, 673, 769, 773, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1091, 1093, 1097, 1109, 1123, 1129, 1153, 1163, 1171

Offset: 1

Author

Antti Karttunen, Jun 01 2004

Keywords

• nonn
• base
• easy

Examples

			73 is in the sequence because 73 is a prime and 73_10 = 1001001_2. '1001001' has four 0's and one 1. - _Indranil Ghosh_, Jan 31 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..20000
• A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Crossrefs

Complement of A095074 in A000040. Subset: A095072. Cf. A095019.

Programs

Mathematica

Reap[Do[p=Prime[k];id=IntegerDigits[p,2];n=Length@id;If[Count[id,0]>n/2,Sow[p]],{k,200}]][[2,1]]
(* Zak Seidov *)
Select[Prime[Range[200]],DigitCount[#,2,0]>DigitCount[#,2,1]&] (* Harvey P. Dale, Nov 28 2024 *)

PARI

B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
if(b0 > b1, return(1);, return(0););};
forprime(x = 2, 1171, if(B(x), print1(x, ", "); ); ); \\ Washington Bomfim, Jan 11 2011

PARI

{forprime(p=2,1171,nB=floor(log(p)/log(2));
sum(i=0,nB,bittest(p,i))<=nB/2&print1(p,","))} \\ Zak Seidov, Jan 11 2011

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("0")>bin(i)[2:].count("1"):
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Jan 31 2017