login
A161152
Positive integers n such that {the number of (non-leading) 0's in the binary representation of n} is coprime to n.
5
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
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
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Jun 03 2009
EXTENSIONS
Extended by Ray Chandler, Jun 11 2009
STATUS
approved