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A212314
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Numbers m such that B(m^3) = 3*B(m), where B(m) is the binary weight of m (A000120).
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3
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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
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OFFSET
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1,2
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COMMENTS
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2*k is a term if and only if k is a term. - Robert Israel, Nov 06 2022
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LINKS
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FORMULA
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MAPLE
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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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PROG
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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))
(PARI) isok(m) = hammingweight(m^3) == 3*hammingweight(m); \\ Michel Marcus, Nov 06 2022
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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