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Search: id:A120858
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| A120858 |
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Dispersion of the Beatty sequence {[r*n]}, where r=3+8^(1/2). |
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6
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| 1, 2, 5, 3, 11, 29, 4, 17, 64, 169, 6, 23, 99, 373, 985, 7, 34, 134, 577, 2174, 5741, 8, 40, 198, 781, 3363, 12671, 33461, 9, 46, 233, 1154, 4552, 19601, 73852, 195025, 10, 52, 268, 1358, 6726, 26531, 114243, 430441, 1136689, 12, 58, 303, 1562
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Every positive integer occurs exactly once and every pair of rows are mutually interspersed. That is, beginning at the first term of any row having greater initial term than that of another row, all the following terms individually separate the individual terms of the other row.
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REFERENCES
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C. Kimberling, The equation (j+k+1)^2-4k=Q*n^2 and related dispersions, preprint.
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LINKS
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N. J. A. Sloane, Classic Sequences.
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FORMULA
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(1) Column 1 is the sequence {[sn]} where 1/r+1/s=1. The numbers in all the other columns, arranged in increasing order, form the sequence {[r*n]}. (2) Every row satisfies these recurrences: x(n+1)=[r*x(n)] and x(n+2)=6*x(n+1)-x(n).
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EXAMPLE
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Northwest corner:
1 5 29 169 985
2 11 64 373 2174
3 17 99 577 3363
4 23 134 781 4552
6 34 198 1154 6726.
In row 1, we have 5=[r], 29=[5r], 169=[29r]; each new
row starts with the least "new" number n, followed
by [nr], [[nr]r], [[[nr]r]r] and so on.
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CROSSREFS
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Cf. A120859, A120860, A120861, A120862, A120863.
Sequence in context: A129198 A122442 A162613 this_sequence A124937 A091265 A028415
Adjacent sequences: A120855 A120856 A120857 this_sequence A120859 A120860 A120861
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Jul 09 2006
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