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.

1, 1, 2, 1, 4, 8, 16, 29, 51, 128, 344, 528, 1863, 5283, 12445

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

Table of n, a(n) for n=1..15.

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: A294061 A113820 A378338 * A303632 A133267 A145864

Adjacent sequences: A319476 A319477 A319478 * A319480 A319481 A319482

Keyword

nonn,more

Author

Peter Kagey, Sep 19 2018

Status

approved