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A005823
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Numbers whose ternary expansion contains no 1's.
(Formerly M1567)
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29
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0, 2, 6, 8, 18, 20, 24, 26, 54, 56, 60, 62, 72, 74, 78, 80, 162, 164, 168, 170, 180, 182, 186, 188, 216, 218, 222, 224, 234, 236, 240, 242, 486, 488, 492, 494, 504, 506, 510, 512, 540, 542, 546, 548, 558, 560, 564, 566, 648, 650, 654, 656, 666, 668, 672, 674
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The set of real numbers between 0 and 1 that contain no 1's in their ternary expansion is the well-known Cantor set with Hausdorff dimension log 2 / log 3.
Complement of A081606. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 23 2003
Numbers n such that the n-th Apery number equals 1 (mod 3) (cf. A005258) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 30 2003
Numbers n such that the n-th central Delannoy number equals 1 (mod 3) (cf. A001850) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 30 2003
Numbers n such that there exists a permutation p_1, ..., p_n of 1, ..., n such that i + p_i is a power of 3 for every i - Ray Chandler (rayjchandler(AT)sbcglobal.net), Aug 3 2004
Subsequence of A125292; A125291(a(n)) = 1 for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 26 2006
A062756(a(n)) = 0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 02 2008
The first 2^n terms of the sequence could be obtained using the Cantor process for the segment [0,3^n-1]. E.g. for n=2 we have [0,{1},2,{3,4,5},6,{7},8]. The numbers outside of braces are the first 4 terms of the sequence. Therefore the terms of the sequence could be named as "Cantor's numbers". - Vladimir Shevelev (shevelev(AT)bgu.ac.il), Jun 13 2008
Subsequence of A154314. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 07 2009]
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REFERENCES
| J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197.
K. J. Falconer, The Geometry of Fractal Sets, Cambridge, 1985; p. 14.
C. Kimberling, Affinely recursive sets and orderings of languages, Discrete Math., 274 (2004), 147-160. [From N. J. A. Sloane, Jan 31 2012]
M. Mendes France and A. J. van der Poorten, From geometry to Euler identities, Theoret. Comput. Sci., 65 (1989), 213-220.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1024
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197.
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FORMULA
| a(2n) = 3a(n), a(2n+1) = 3a(n)+2.
a(n) = Sum_{k = 1..n} 1 + 3^A007814(k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 09 2005
If the offset were changed to zero, then: a(0)=0, a(n+1)=f(a(n)+1,f(a(n)+1) where f(x,y) = if x<3 and x<>1 then y else if x mod 3 = 1 then f(y+1,y+1) else f(floor(x/3),y). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 02 2008
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MATHEMATICA
| Select[ Range[ 0, 729 ], (Count[ IntegerDigits[ #, 3 ], 1 ]==0)& ]
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CROSSREFS
| Twice A005836. Cf. A032924, A014263, A007089, A062756, A061392, A005836, A001196, A097252-A097262.
Sequence in context: A182629 A183212 A053355 * A178758 A024431 A152598
Adjacent sequences: A005820 A005821 A005822 * A005824 A005825 A005826
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit
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EXTENSIONS
| More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Mar 24 2002
Offset corrected by N. J. A. Sloane (njas(AT)research.att.com), Mar 02 2008. This may require some of the formulae to be adjusted.
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