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

1,1

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A031432 A157474 A024215 * A095072 A180529 A214032

Adjacent sequences: A095068 A095069 A095070 * A095072 A095073 A095074

Keyword

nonn,base,easy

Author

Antti Karttunen, Jun 01 2004

Status

approved