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A020914
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Number of digits in the base-2 representation of 3^n.
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30
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1, 2, 4, 5, 7, 8, 10, 12, 13, 15, 16, 18, 20, 21, 23, 24, 26, 27, 29, 31, 32, 34, 35, 37, 39, 40, 42, 43, 45, 46, 48, 50, 51, 53, 54, 56, 58, 59, 61, 62, 64, 65, 67, 69, 70, 72, 73, 75, 77, 78, 80, 81, 83, 85, 86, 88, 89, 91, 92, 94, 96, 97, 99, 100, 102, 104, 105, 107
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OFFSET
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0,2
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COMMENTS
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Also, numbers k such that the first digit in the ternary expansion of 2^k is 1. - Mohammed Bouayoun (Mohammed.bouayoun(AT)sanef.com), Apr 24 2006
a(n) is the smallest integer such that n/a(n) < log_2(3). - Trevor G. Hyde (thyde12(AT)amherst.edu), Jul 31 2008
This sequence represents allowable values of the "dropping time" in the Collatz (3x+1) problem when iterated according to the function f(n) := n/2 if n is even, (3n+1)/2 otherwise, as tabulated in A126241. There is one exception, A126241(1), which has been set to zero by convention. - K. Spage, Oct 22 2009
An integer k is a term of A020914 if and only if floor(k*(1 + log(2)/log(3))) - abs(k-1)*(1 + log(2)/log(3)) - 1 >= 0. - K. Spage, Oct 22 2009
Also smallest k such that ceiling(2^k / 3^n) = 2. - Michel Lagneau, Jan 31 2012
Also the number of powers of two less than or equal to 3^n. - Robert G. Wilson v, May 25 2014
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LINKS
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FORMULA
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a(n) = floor(1 + n*log(3)/log(2)). - K. Spage, Oct 22 2009
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MAPLE
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A020914 :=n->nops(convert(3^n, base, 2)):
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MATHEMATICA
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PROG
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(PARI) for(n=0, 100, print1(floor(1+n*log(3)/log(2)), ", ")) \\ K. Spage, Oct 22 2009
(Haskell)
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CROSSREFS
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Cf. A020857 (decimal expansion of log_2(3)).
Cf. A204399 (essentially the same).
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KEYWORD
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nonn,base,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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