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Search: id:A113497
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| A113497 |
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Ascending descending base exponent transform of a simple periodic sequence (A000034). |
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+0
2
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| 1, 3, 6, 6, 11, 9, 16, 12, 21, 15, 26, 18, 31, 21, 36, 24, 41, 27, 46, 30, 51, 33, 56, 36, 61, 39, 66, 42, 71, 45, 76, 48, 81, 51, 86, 54, 91, 57, 96
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A000034 = 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, ... = continued fraction for (sqrt(3)+1)/2 (cf. A040001) = base 3 digital root of n+1. In general, the ascending descending base exponent transform of any simple periodic sequence can be written as a periodic set of interleaved sequences.
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FORMULA
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a(n) = SUM[from i = 1 to n] (A000034(i))^(A000034(n-i+1)). a(2n) = 3n. a(2n+1) = 5n+1.
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EXAMPLE
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a(1) = 1^1 = 1.
a(2) = 1^2 + 2^1 = 3.
a(3) = 1^1 + 2^2 + 1^1 = 6.
a(4) = 1^2 + 2^1 + 1^2 + 2^1 = 6.
a(5) = 1^1 + 2^2 + 1^1 + 2^2 + 1^1 = 11.
a(6) = 1^2 + 2^1 + 1^2 + 2^1 + 1^2 + 2^1 = 9.
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CROSSREFS
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Cf. A000034, A113320, A005408, A113122, A113153, A113154, A113336, A113271, A113258, A113257, A113231, A087316, A113208.
Sequence in context: A002853 A135610 A157018 this_sequence A158662 A119980 A066779
Adjacent sequences: A113494 A113495 A113496 this_sequence A113498 A113499 A113500
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 10 2006
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