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Search: id:A115352
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| A115352 |
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The sequence is the concatenation of finite strings S_0, S_1, S_2, ..., where S_0 = {0} and for k >= 1, S_k is obtained from S_{k-1} by inserting the numbers 2^(k-1) through 2^k-1 after the initial 0. |
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+0
1
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| 0, 0, 1, 0, 2, 3, 1, 0, 4, 5, 6, 7, 2, 3, 1, 0, 8, 9, 10, 11, 12, 13, 14, 15, 4, 5, 6, 7, 2, 3, 1, 0, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 8, 9, 10, 11, 12, 13, 14, 15, 4, 5, 6, 7, 2, 3, 1, 0, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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For example, for k = 3, take S_2 = {0,2,3,1} and insert 2^2 through 2^3-1 after the 0, so that S_3 = {0,4,5,6,7,2,3,1}. The string S_k has length 2^k.
A self-similar fractal sequence.
This is the sequence g_n at the end of Section 2 of Levine's paper. The paper also continues several other sequences that are probably not in the OEIS at present
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REFERENCES
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L. Levine, Fractal sequences and restricted Nim, Ars Comb., to appear (2006).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1022
L. Levine, Fractal sequences and restricted Nim
L. Levine, Home Page
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FORMULA
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If n=2^m-1, then a(n)=0; for all other terms, write n in binary, collapse the initial segment of 1's to a single 1 and delete the first 0. For example, a(25)=a(11001)=101=5. - Lionel Levine (levine(AT)Math.Berkeley.EDU), May 04 2006
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EXAMPLE
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The first few strings S_0, S_1, S_2, ... are as follows:
0
0,1
0,2,3,1
0,4,5,6,7,2,3,1
0,8,9,10,11,12,13,14,15,4,5,6,7,2,3,1
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CROSSREFS
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See A025480 for a similar sequence.
Sequence in context: A130717 A137396 A167666 this_sequence A038554 A100329 A081247
Adjacent sequences: A115349 A115350 A115351 this_sequence A115353 A115354 A115355
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KEYWORD
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nonn,tabf
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mar 10 2006
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(at)rgwv.com), Apr 11 2006
Further edited by N. J. A. Sloane (njas(AT)research.att.com), Jan 16 2009
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