A161154 Positive integers n such that both {the number of (non-leading) 0's in the binary representation of n} is coprime to n and {the number of 1's in the binary representation of n} is coprime to n.

1, 2, 5, 8, 9, 11, 13, 14, 17, 19, 23, 25, 27, 29, 32, 33, 35, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 51, 52, 53, 56, 57, 59, 61, 62, 67, 71, 73, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 107, 109, 113, 117, 119, 121, 125, 128, 131, 133, 134, 135, 137, 139, 141

Offset: 1

Author

Leroy Quet, Jun 03 2009

Keywords

• base
• nonn

Comments

1 is the only integer of the form 2^k - 1 (k>=0) included in this sequence, because such integers contain no binary 0's, and 0 is considered here to be coprime only to 1.

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A094387, A161152, A161153, A161155, A161156.

Programs

Mathematica

bcpQ[n_]:=Module[{ones=DigitCount[n,2,1],zeros=DigitCount[n,2,0]}, And@@ CoprimeQ[ {ones,zeros},n]]; Select[Range[150],bcpQ] (* Harvey P. Dale, Feb 19 2012 *)

PARI

b0(n) = if(n<1, 0, b0(n\2) + 1 - n%2);
b1(n) = if(n<1, 0, b1(n\2) + n%2);
for (n=1, 141, if(gcd(b0(n),n)==1 && gcd(b1(n),n)==1, print1(n", "))) \\ Indranil Ghosh, Mar 08 2017

Python

from math import gcd
i=j=1
while j<=100:
    if gcd(bin(i)[2:].count("0"),i)==1==gcd(bin(i)[2:].count("1"),i):
        print(j, i)
        j+=1
    i+=1 # Indranil Ghosh, Mar 08 2017

Extensions

Extended by Ray Chandler, Jun 11 2009