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A020914
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Number of digits in base 2 representation of 3^n.
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17
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also, numbers n such that the first digit in ternary expansion on 2^n 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 which is A126241(1), which has been set to zero by convention. [From K Spage (kevspage2001(AT)yahoo.co.uk), Oct 22 2009]
An integer (x) is a member of A020914 if and only if floor(x*(1+log(2)/log(3)))-abs(x-1)*(1+log(2)/log(3))-1 >= 0. [From K. Spage (kevspage2001(AT)yahoo.co.uk), Oct 22 2009]
Also smallest k such that ceil(2^k /3^n) = 2. [From Michel Lagneau, Jan 31 2012]
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LINKS
| T. D. Noe, Table of n, a(n) for n = 0..1000
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FORMULA
| a(n) = floor(1+n*ln(3)/ln(2)) [From K Spage (kevspage2001(AT)yahoo.co.uk), Oct 22 2009]
a(0)=1,a(n+1)=a(n)+A022921(n) [From K. Spage (kevspage2001(AT)yahoo.co.uk), Oct 23 2009]
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MAPLE
| a:=n->nops(convert(3^n, base, 2)): seq(a(n), n=0..70); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 30 2006
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MATHEMATICA
| Table[Length[IntegerDigits[3^n, 2]], {n, 0, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 19 2006
Do[If[First[IntegerDigits[2^n, 3]] == 1, Print[n]], {n, 1, 100}] - Mohammed Bouayoun (Mohammed.bouayoun(AT)sanef.com), Apr 24 2006
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PROG
| (PARI) for(n=0, 100, print1(floor(1+n*log(3)/log(2)), ", ")) [From K Spage (kevspage2001(AT)yahoo.co.uk), Oct 22 2009]
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CROSSREFS
| Cf. a(n)= A122437(n-1)-n [From K. Spage (kevspage2001(AT)yahoo.co.uk), Oct 23 2009]
A098294(n) = a(n)+n for n>0 [from Mike Winkler (mike.winkler(at)gmx.de), Dec 31 2010]
Sequence in context: A102338 A139449 A204399 * A195176 A195126 A047496
Adjacent sequences: A020911 A020912 A020913 * A020915 A020916 A020917
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KEYWORD
| nonn,base,easy
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 19 2006
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