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Search: id:A133108
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| A133108 |
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Representation of a dense para-sequence. |
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+0
2
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| 1, 2, 3, 4, 1, 5, 6, 2, 7, 8, 9, 10, 3, 11, 12, 4, 13, 14, 1, 15, 16, 5, 17, 18, 6, 19, 20, 2, 21, 22, 7, 23, 24, 8, 25, 26, 27, 28, 9, 29, 30, 10, 31, 32, 3, 33, 34, 11, 35, 36, 12, 37, 38, 4, 39, 40, 13, 41, 42, 14, 43, 44, 1, 45, 46, 15, 47, 48, 16, 49, 50, 5, 51, 52, 17, 53, 54, 18
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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(1) A fractal sequence. (2) The para-sequence may be regarded as a sort of "limit" of the concatenated segments. The para-sequence (itself not a sequence) is dense in the sense that every pair of terms i and j are separated by another term (and hence separated by infinitely many terms. (3) The para-sequence accounts for positions of triadic rational numbers in the following way: 1/3 < 2/3 matches the segment 1,2; 1/9 < 2/9 < 1/3 < 4/9 < 5/9 < 2/3 < 7/9 < 8/9 matches the segment 3,4,1,5,6,2,7,8, etc.
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REFERENCES
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C. Kimberling, Proper self-containing sequences, fractal sequences, and para-sequences, preprint, 2007.
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FORMULA
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Start with initial segment 1,2 and isolate them using 3-to-8 like this: 3,4,1,5,6,2,7,8. (This is the 2nd segment.) Then isolate those using 9-to-26, like this: 9,10,3,11,12,4,13,14,1,...8,25,26. (This is the 3rd segment.) Continue, and concatenate.
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EXAMPLE
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The first segment is 1,2; the 2nd is 3,4,1,5,6,2,7,8; the
4th begins with 27,28,9 and ends with 26,79,80.
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CROSSREFS
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Cf. A131987.
Adjacent sequences: A133105 A133106 A133107 this_sequence A133109 A133110 A133111
Sequence in context: A115994 A071437 A129709 this_sequence A055441 A104717 A067003
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Sep 12 2007
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