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
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
select(n -> convert(convert(n^3,base,2),`+`) = 3*convert(convert(n,base,2),`+`), [$0..1000]); # Robert Israel, Nov 06 2022
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PARI
isok(m) = hammingweight(m^3) == 3*hammingweight(m); \\ Michel Marcus, Nov 06 2022
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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
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