

A161154


Positive integers n such that both {the number of (nonleading) 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.


5



1, 2, 5, 8, 9, 11, 13, 14, 17, 19, 23, 25, 27, 29, 32, 33, 35, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 51, 52, 53, 56, 57, 59, 61, 62, 67, 71, 73, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 101, 103, 107, 109, 113, 117, 119, 121, 125, 128, 131, 133, 134, 135, 137, 139, 141
(list;
graph;
refs;
listen;
history;
text;
internal format)



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

Indranil Ghosh, Table of n, a(n) for n = 1..1000


MATHEMATICA

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 *)


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, 141, if(gcd(b0(n), n)==1 && gcd(b1(n), 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:
........print str(j)+" "+str(i)
........j+=1
....i+=1 # Indranil Ghosh, Mar 08 2017


CROSSREFS

Cf. A094387, A161152, A161153, A161155, A161156.
Sequence in context: A231756 A212591 A153275 * A174438 A176061 A183234
Adjacent sequences: A161151 A161152 A161153 * A161155 A161156 A161157


KEYWORD

base,nonn


AUTHOR

Leroy Quet, Jun 03 2009


EXTENSIONS

Extended by Ray Chandler, Jun 11 2009


STATUS

approved



