A319479 - OEIS

%I #19 Sep 23 2018 01:56:47

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

%N 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.

%C 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).

%e For n = 5, a(5) = 4 because letting a(5) = 1, 2, or 3 creates barycenter collisions:

%e +-----------+----------------+--------------------------------+------------+

%e | candidate | set 1          | set 2                          | barycenter |

%e +-----------+----------------+--------------------------------+------------+

%e | (5, 1)    | (1, 1); (5, 1) | (1, 1); (2, 1); (4, 1); (5, 1) | (6, 1)     |

%e | (5, 2)    | (2, 1); (5, 2) | (2, 1); (3, 2); (4, 1); (5, 2) | (3.5, 1.5) |

%e | (5, 3)    | (1, 1); (5, 3) | (1, 1); (3, 2); (5, 3)         | (3, 2)     |

%e +-----------+----------------+--------------------------------+------------+

%e And a(5) = 4 creates no such problems.

%Y Cf. A285491.

%K nonn,more

%O 1,3

%A _Peter Kagey_, Sep 19 2018