A161154 - OEIS

%I #17 Apr 30 2021 16:33:42

%S 1,2,5,8,9,11,13,14,17,19,23,25,27,29,32,33,35,37,38,39,41,43,44,45,

%T 47,49,50,51,52,53,56,57,59,61,62,67,71,73,77,79,83,85,87,89,91,93,95,

%U 97,101,103,107,109,113,117,119,121,125,128,131,133,134,135,137,139,141

%N Positive integers n such that both {the number of (non-leading) 0's in the binary representation of n} is coprime to n and {the number of 1's 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="/A161154/b161154.txt">Table of n, a(n) for n = 1..1000</a>

%t bcpQ[n_]:=Module[{ones=DigitCount[n,2,1],zeros=DigitCount[n,2,0]}, And@@ CoprimeQ[ {ones,zeros},n]]; Select[Range[150],bcpQ] (* _Harvey P. Dale_, Feb 19 2012 *)

%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, 141, if(gcd(b0(n),n)==1 && gcd(b1(n),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==gcd(bin(i)[2:].count("1"),i):

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

%o         j+=1

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

%Y Cf. A094387, A161152, A161153, A161155, A161156.

%K base,nonn

%O 1,2

%A _Leroy Quet_, Jun 03 2009

%E Extended by _Ray Chandler_, Jun 11 2009