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A319479 Lexicographically earliest sequence such that for every n and every sequence 1 <= b_1 < b_2 < ... < b_t = n, the values of barycenter((b_1, a(b_1)), (b_2, a(b_2)), ..., (b_t, a(b_t))) are distinct. 0
1, 1, 2, 1, 4, 8, 16, 29, 51, 128, 344, 528, 1863, 5283, 12445 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The barycenter of the points {(x_1, y_1), (x_2, y_2), ..., (x_k, y_k)} is given by the average of the x and y coordinates: (Sum_{i=1..k} x_i/k, Sum_{i=1..k} y_i/k).
LINKS
EXAMPLE
For n = 5, a(5) = 4 because letting a(5) = 1, 2, or 3 creates barycenter collisions:
+-----------+----------------+--------------------------------+------------+
| candidate | set 1 | set 2 | barycenter |
+-----------+----------------+--------------------------------+------------+
| (5, 1) | (1, 1); (5, 1) | (1, 1); (2, 1); (4, 1); (5, 1) | (6, 1) |
| (5, 2) | (2, 1); (5, 2) | (2, 1); (3, 2); (4, 1); (5, 2) | (3.5, 1.5) |
| (5, 3) | (1, 1); (5, 3) | (1, 1); (3, 2); (5, 3) | (3, 2) |
+-----------+----------------+--------------------------------+------------+
And a(5) = 4 creates no such problems.
CROSSREFS
Cf. A285491.
Sequence in context: A294104 A294061 A113820 * A303632 A133267 A145864
KEYWORD
nonn,more
AUTHOR
Peter Kagey, Sep 19 2018
STATUS
approved

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Last modified April 22 08:00 EDT 2024. Contains 371892 sequences. (Running on oeis4.)