A161152 Positive integers n such that {the number of (non-leading) 0's in the binary representation of n} is coprime to n.

1, 2, 5, 6, 8, 9, 11, 13, 14, 17, 19, 20, 21, 23, 25, 27, 29, 30, 32, 33, 35, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 51, 52, 53, 55, 56, 57, 59, 61, 62, 66, 67, 68, 69, 71, 72, 73, 77, 79, 81, 83, 85, 86, 87, 89, 91, 92, 93, 95, 96, 97, 101, 103, 106, 107, 109, 111, 113, 115

Offset

1,2

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

Example

13 is in the sequence because the number of non-leading 0 s in the binary representation of 13 is 1 (13_10 = 1101_2) and gcd(1, 13) = 1. - Indranil Ghosh, Mar 08 2017

Mathematica

Select[Range[115], GCD[DigitCount[#, 2, 0], #] == 1 &] (* Indranil Ghosh, Mar 08 2017 *)

Prog

(PARI) b(n) = if(n<1, 0, b(n\2) + 1 - n%2);
for (n=1, 115, if(gcd(b(n), n)==1, print1(n", "))); \\ Indranil Ghosh, Mar 08 2017
(Python)
from fractions import gcd
i=j=1
while j<=100:
    if gcd(bin(i)[2:].count("0"), i)==1:
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Mar 08 2017

Crossrefs

Cf. A094387, A161153, A161154, A161155, A161156.

Sequence in context: A157850 A049636 A045573 * A261905 A340602 A350945

Adjacent sequences: A161149 A161150 A161151 * A161153 A161154 A161155

Keyword

base,nonn

Author

Leroy Quet, Jun 03 2009

Extensions

Extended by Ray Chandler, Jun 11 2009

Status

approved