A212314 Numbers m such that B(m^3) = 3*B(m), where B(m) is the binary weight of m (A000120).

0, 5, 9, 10, 17, 18, 20, 33, 34, 36, 39, 40, 49, 65, 66, 68, 69, 72, 78, 80, 98, 105, 129, 130, 132, 135, 136, 138, 144, 156, 160, 169, 196, 199, 209, 210, 229, 257, 258, 260, 263, 264, 270, 272, 276, 277, 288, 291, 297, 312, 313, 320, 338, 359, 365, 392, 395, 398, 418

Offset: 1

Author

Alex Ratushnyak, Oct 24 2013

Keywords

• nonn
• base
• easy

Comments

2*k is a term if and only if k is a term. - Robert Israel, Nov 06 2022

Links

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

Crossrefs

Cf. A000120, A077436, A083567, A118655, A212315.

Includes A136318.

Programs

Maple

select(n -> convert(convert(n^3,base,2),`+`) = 3*convert(convert(n,base,2),`+`), [$0..1000]); # Robert Israel, Nov 06 2022

PARI

isok(m) = hammingweight(m^3) == 3*hammingweight(m); \\ Michel Marcus, Nov 06 2022

Python

import math
for n in range(10000):
    c1 = c2 = 0
    t = n
    while t:
        c1+=t&1
        t>>=1
    t = n*n*n
    while t:
        c2+=t&1
        t>>=1
    if c1*3==c2: print(str(n), end=',')

Sage

s = lambda n: sum((n^3).digits(2)) - 3*sum(n.digits(2))
[n for n in (0..418) if s(n)==0]  # Peter Luschny, Oct 24 2013

Formula

A000120(a(n)^3) = A000120(a(n)) * 3.