A144754 Integers that have a prime number of 0's in their binary expansion.

4, 8, 9, 10, 12, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 32, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 56, 57, 58, 60, 65, 66, 68, 71, 72, 75, 77, 78, 79, 80, 83, 85, 86, 87, 89, 90, 91, 92, 93, 94, 96, 99, 101, 102, 103, 105, 106, 107, 108, 109, 110

Offset: 1

Author

Leroy Quet, Sep 20 2008

Keywords

• base
• nonn

Examples

			66 written in binary is 1000010. This has five 0's and five is a prime. So 66 is included in the sequence.
		

Links

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

Crossrefs

Cf. A052294.

Programs

Mathematica

Select[Range@ 120, PrimeQ@ DigitCount[#, 2, 0] &] (* Michael De Vlieger, Oct 26 2017 *)

PARI

isok(n) = isprime(#binary(n) - hammingweight(n)); \\ Michel Marcus, Feb 23 2016

Python

from sympy import isprime
i=j=1
while j<=250:
    if isprime(bin(i)[2:].count("0")):
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Feb 03 2017

Extensions

Many more terms from Reikku Kulon, Sep 21 2008

Name edited by Michel Marcus, Apr 30 2021