A095074 Primes in whose binary expansion the number of 0-bits is less than or equal to number of 1-bits.

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 71, 79, 83, 89, 101, 103, 107, 109, 113, 127, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 271, 283, 307, 311, 313, 317, 331, 347

Offset

1,1

Links

Indranil Ghosh, Table of n, a(n) for n = 1..25000

A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Example

From Indranil Ghosh, Feb 03 2017 (Start):
29 is in the sequence because 29_10 = 11101_2. '11101' has one 0 and three 1's.
37 is in the sequence because 37_10 = 100101_2. '100101' has three 1's and 3 0's. (Stop)

Mathematica

Select[Prime[Range[50]], DigitCount[#, 2, 0] <= DigitCount[#, 2, 1] &] (* Alonso del Arte, Jan 11 2011 *)

Prog

(PARI)forprime(p=2, 347, v=binary(p); s=0; for(k=1, #v, s+=if(v[k]==0, +1, -1)); if(s<=0, print1(p, ", "))) \\ Washington Bomfim, Jan 13 2011
(Python)
from sympy import isprime
i=1
j=1
while j<=25000:
    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, Feb 03 2017

Crossrefs

Complement of A095071 in A000040. Differs from A057447 first time at n=18, where a(n)=71, while A057447(18)=67. Cf. A095054.

Sequence in context: A316968 A105049 A057447 * A042987 A089189 A097375

Adjacent sequences: A095071 A095072 A095073 * A095075 A095076 A095077

Keyword

nonn,base

Author

Antti Karttunen, Jun 01 2004

Status

approved