OFFSET
1,1
COMMENTS
1 is the only integer of the form 2^k -1 (k>=0) which is coprime to the number of 0's in its binary representation, 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
MATHEMATICA
Select[Range[393], GCD[DigitCount[#, 2, 0] , #]==1 && GCD[DigitCount[#, 2, 1], #] == 1 && GCD[Length[IntegerDigits[#, 2]], #] != 1 &] (* Indranil Ghosh, Mar 08 2017 *)
PROG
(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, 393, if(gcd(b0(n), n) == 1 && gcd(b1(n), n) == 1 && gcd(#digits(n, 2), n) != 1, print1(n", "))); \\ Indranil Ghosh, Mar 08 2017
(Python)
from fractions import gcd
i=j=1
while j<=1000:
if gcd(bin(i)[2:].count("0"), i)==1 and gcd(bin(i)[2:].count("1"), i)==1 and gcd(len(bin(i)[2:]), i)!=1:
print(str(i), end=", ")
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