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.

1, 5, 9, 11, 13, 17, 19, 23, 27, 29, 35, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 85, 87, 89, 93, 95, 97, 101, 103, 107, 109, 113, 117, 121, 125, 131, 133, 135, 137, 139, 141, 143, 147, 149, 151, 153, 157, 161, 163, 165, 167, 169, 173, 175, 177, 179, 181

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

Select[Range[181], GCD[DigitCount[#, 2, 0] , #]==1 && GCD[DigitCount[#, 2, 1], #]==1 && GCD[Length[IntegerDigits[#, 2]], #]==1 &] (* Indranil Ghosh, Mar 08 2017 *)

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, 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
(Python)
from fractions import gcd
i=j=1
while j<=100:
    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:
        print(str(j)+" "+str(i))
        j+=1
    i+=1 # Indranil Ghosh, Mar 08 2017

Crossrefs

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

Sequence in context: A043757 A043766 A063479 * A337920 A314585 A078621

Adjacent sequences: A161152 A161153 A161154 * A161156 A161157 A161158

Keyword

base,nonn

Author

Leroy Quet, Jun 03 2009

Extensions

Extended by Ray Chandler, Jun 11 2009

Status

approved