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Search: id:A107284
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| A107284 |
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a(n)/4^n is the measure of the subset of [0,1] remaining when all intervals of the form [b/2^m - 1/2^(2m), b/2^m + 1/2^(2m)] have been removed, with b and m positive integers, b<2^m and m<=n. |
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1
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| 1, 2, 6, 20, 74, 284, 1116, 4424, 17622, 70340, 281076, 1123736, 4493828, 17973080, 71887896, 287542736, 1150153322, 4600578044, 18402241836, 73608826664, 294435025580, 1177739540168, 4710957036936, 18843825900272, 75375299107260
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OFFSET
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0,2
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COMMENT
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Removing all such intervals (without an upper limit on n) leaves a nowhere dense subset of [0,1]. It is of positive measure, namely 0.2677868402178891123766714035843..., the limit of a(n)/4^n. This is the same as the limit of A003000(n)/2^n and of A045690(n)/2^n, and half the limit of A105284(n)/4^n.
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FORMULA
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a(n) =4a(n-1)-A003000(n) =2*A105284(n-1). a(2n+1)=6a(2n)-8a(2n-1); a(4n)=6a(4n-1)-8a(4n-2)-a(n); a(4n+2)=6a(4n+1)-8a(4n)-2a(n).
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EXAMPLE
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At the start the interval [0,1] has measure 1=1/1. The first step removes the interval [1/4,3/4], leaving a subset with measure of 1/2=2/4. The second step in addition removes the intervals [3/16,1/4) and (3/4,13/16], leaving a subset with measure of 3/8=6/16. The third step in addition removes the intervals [7/64,9/64] and [55/64,57/64], leaving a subset with measure of 5/16=20/64.
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CROSSREFS
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Sequence in context: A052884 A061396 A104632 this_sequence A006850 A034010 A135588
Adjacent sequences: A107281 A107282 A107283 this_sequence A107285 A107286 A107287
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), May 19 2005
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