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Search: id:A055247
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| A055247 |
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Related to A055246 and A005836. Used for boundaries of open intervals which have to be erased in the Cantor middle third set construction. |
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2
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| 1, 2, 7, 8, 19, 20, 25, 26, 55, 56, 61, 62, 73, 74, 79, 80, 163, 164, 169, 170, 181, 182, 187, 188, 217, 218, 223, 224, 235, 236, 241, 242, 487, 488, 493, 494, 505, 506, 511, 512, 541, 542, 547, 548, 559, 560, 565, 566, 649, 650, 655, 656
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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At step number k >= 1 the 2^(k-1) open intervals which are erased from [0,1] in the Cantor middle third set construction are: I(k,n)=(a(2*n-1)/3^k,a(2*n)/3^k), n=1,.,2^(k-1).
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FORMULA
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a(n)= A055246((n+1)/2) if n odd, a(n)= A055246(n/2)+1 if n even. A055246(n)= 1+6*A005836(n-1), n >= 1.
a(1) = 1, a(n) = 3^ceiling( log_2( n ) ) - a( 2^ceiling( log_2( n ) ) + 1 - n ). - Juan Jose Alba Gonzalez (jjalba(AT)gmail.com), May 16 2006
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EXAMPLE
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k=1: (1/3, 2/3); k=2: (1/9, 2/9), (7/9, 8/9); k=3: (1/27, 2/27), (7/27, 8/27), (19/27, 20/27), (25/27, 26/27); ...
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CROSSREFS
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Cf. A005836, A055246.
Adjacent sequences: A055244 A055245 A055246 this_sequence A055248 A055249 A055250
Sequence in context: A080572 A032689 A101518 this_sequence A015617 A026579 A054601
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 23 2000
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