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

1,1

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.

Example

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

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 *)

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(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

Crossrefs

Intersection of A000040 and A072600.

Complement of A095075 in A000040.

Subsequence: A095073.

Cf. A095020.

Sequence in context: A138004 A045395 A191377 * A350577 A079733 A179538

Adjacent sequences: A095067 A095068 A095069 * A095071 A095072 A095073

Keyword

nonn,easy,base

Author

Antti Karttunen, Jun 01 2004

Status

approved