A161155 - OEIS

%I #14 Apr 30 2021 16:28:56

%S 1,5,9,11,13,17,19,23,27,29,35,37,41,43,47,49,53,59,61,67,71,73,79,83,

%T 85,87,89,93,95,97,101,103,107,109,113,117,121,125,131,133,135,137,

%U 139,141,143,147,149,151,153,157,161,163,165,167,169,173,175,177,179,181

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

%C 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.

%H Indranil Ghosh, <a href="/A161155/b161155.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Range[181], GCD[DigitCount[#,2,0] , #]==1 && GCD[DigitCount[#,2,1],#]==1 && GCD[Length[IntegerDigits[#,2]],#]==1 &] (* _Indranil Ghosh_, Mar 08 2017 *)

%o (PARI) b0(n) = if(n<1, 0, b0(n\2) + 1 - n%2);

%o b1(n) = if(n<1, 0, b1(n\2) + n%2);

%o for (n=1, 181, if(gcd(b0(n), n) == 1 && gcd(b1(n), n) == 1 && gcd(#digits(n, 2), n) == 1, print1(n", "))) \\ _Indranil Ghosh_, Mar 08 2017

%o (Python)

%o from fractions import gcd

%o i=j=1

%o while j<=100:

%o     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:

%o         print(str(j)+" "+str(i))

%o         j+=1

%o     i+=1 # _Indranil Ghosh_, Mar 08 2017

%Y Cf. A094387, A161152, A161153, A161154, A161156.

%K base,nonn

%O 1,2

%A _Leroy Quet_, Jun 03 2009

%E Extended by _Ray Chandler_, Jun 11 2009