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

1,1

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A052294.

Sequence in context: A193166 A155101 A158582 * A080970 A288862 A274584

Adjacent sequences: A144751 A144752 A144753 * A144755 A144756 A144757

Keyword

base,nonn

Author

Leroy Quet, Sep 20 2008

Extensions

Many more terms from Reikku Kulon, Sep 21 2008

Name edited by Michel Marcus, Apr 30 2021

Status

approved