cp's OEIS Frontend

A161155 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.

%I A161155 #18 Jun 28 2025 11:16:21
%S A161155 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 A161155 85,87,89,93,95,97,101,103,107,109,113,117,121,125,131,133,135,137,
%U A161155 139,141,143,147,149,151,153,157,161,163,165,167,169,173,175,177,179,181
%N A161155 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 A161155 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 A161155 Indranil Ghosh, <a href="/A161155/b161155.txt">Table of n, a(n) for n = 1..1000</a>
%t A161155 Select[Range[181], GCD[DigitCount[#,2,0] , #]==1 && GCD[DigitCount[#,2,1],#]==1 && GCD[Length[IntegerDigits[#,2]],#]==1 &] (* _Indranil Ghosh_, Mar 08 2017 *)
%o A161155 (PARI) b0(n) = if(n<1, 0, b0(n\2) + 1 - n%2);
%o A161155 b1(n) = if(n<1, 0, b1(n\2) + n%2);
%o A161155 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 A161155 (Python)
%o A161155 from math import gcd
%o A161155 i=j=1
%o A161155 while j<=100:
%o A161155     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 A161155         print(j, i)
%o A161155         j+=1
%o A161155     i+=1 # _Indranil Ghosh_, Mar 08 2017
%Y A161155 Cf. A094387, A161152, A161153, A161154, A161156.
%K A161155 base,nonn
%O A161155 1,2
%A A161155 _Leroy Quet_, Jun 03 2009
%E A161155 Extended by _Ray Chandler_, Jun 11 2009