A161154 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.

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

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<=100:
    if gcd(bin(i)[2:].count("0"), i)==1==gcd(bin(i)[2:].count("1"), i):
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Mar 08 2017

Crossrefs

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

Sequence in context: A212591 A153275 A362310 * 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