

A120858


Dispersion of the Beatty sequence {[r*n]}, where r=3+8^(1/2).


5



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
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OFFSET

1,2


COMMENTS

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.


REFERENCES

Clark Kimberling, The equation (j+k+1)^24*k=Q*n^2 and related dispersions, Journal of Integer Sequences 10 (2007, Article 07.2.7) 117.


LINKS

Table of n, a(n) for n=1..49.
N. J. A. Sloane, Classic Sequences.


FORMULA

(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).


EXAMPLE

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.


CROSSREFS

Cf. A120859, A120860, A120861, A120862, A120863.
Sequence in context: A122442 A225258 A162613 * A124937 A279342 A169852
Adjacent sequences: A120855 A120856 A120857 * A120859 A120860 A120861


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Jul 09 2006


STATUS

approved



