A381754 Numbers k such that k and 3*k have the same number of zeros in their binary expansions.

0, 1, 2, 4, 8, 16, 19, 32, 35, 38, 39, 53, 64, 67, 70, 71, 76, 78, 79, 101, 105, 106, 117, 128, 131, 134, 135, 140, 142, 143, 152, 156, 158, 159, 197, 201, 202, 209, 210, 212, 229, 233, 234, 245, 256, 259, 262, 263, 268, 270, 271, 280, 284, 286, 287, 301, 304

Offset: 1

Author

Barak Manos, Mar 06 2025

Keywords

• nonn
• base
• easy

Comments

If n is in the sequence, so is 2n, hence the sequence is infinite. - Charles R Greathouse IV, Mar 06 2025

This sequence corresponds to the numbers m such that A381934(m) <= 3. - Rémy Sigrist, Mar 12 2025

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023416, A077459, A381934.

Programs

Maple

filter:= proc(n) numboccur(0,convert(n,base,2)) = numboccur(0,convert(3*n,base,2)) end proc:
select(filter, [$0..400]); # Robert Israel, Apr 07 2025

Mathematica

Select[Range[0, 320], Equal @@ DigitCount[{#, 3*#}, 2, 0] &] (* Amiram Eldar, Mar 06 2025 *)

PARI

nz(n) = if(n == 0, 1, 1+logint(n, 2) - hammingweight(n))
is(n)=nz(n)==nz(3*n) \\ Charles R Greathouse IV, Mar 06 2025

Python

def ok(n): return bin(n).count('0') == bin(n * 3).count('0')