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A011754
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Number of ones in the binary expansion of 3^n.
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11
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1, 2, 2, 4, 3, 6, 6, 5, 6, 8, 9, 13, 10, 11, 14, 15, 11, 14, 14, 17, 17, 20, 19, 22, 16, 18, 24, 30, 25, 25, 25, 26, 26, 34, 29, 32, 27, 34, 36, 32, 28, 39, 38, 39, 34, 34, 45, 38, 41, 33, 41, 46, 42, 35, 39, 42, 39, 40, 42, 48, 56, 56, 49, 57, 56, 51, 45, 47, 55, 55, 64, 68, 58
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OFFSET
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0,2
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COMMENTS
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Conjecture: a(n)/n tends to log(3)/(2*log(2)) = 0.792481250... (A094148). - Ed Pegg Jr, Dec 05 2002
Senge & Straus prove that for every m, there is some N such that for all n > N, a(n) > m. Dimitrov & Howe make this effective, proving that for n > 25, a(n) > 22. - Charles R Greathouse IV, Aug 23 2021
Ed Pegg's conjecture means that about half of the bits of 3^n are nonzero. It appears that the same is true for 5^n (A000351, cf. A118738) and 7^n (A000420). - M. F. Hasler, Apr 17 2024
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REFERENCES
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S. Wolfram, "A new kind of science", p. 903.
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LINKS
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FORMULA
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MAPLE
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f:= n -> convert(convert(3^n, base, 2), `+`):
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,nice,easy,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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