A300670 Table read by antidiagonals: the n-th row is the lexicographically earliest sequence such that no k + 2 points of ((1, a(1)), (2, a(2)), ...) lie on a polynomial of degree k for k < n.

1, 2, 1, 3, 2, 1, 4, 4, 2, 1, 5, 3, 4, 2, 1, 6, 6, 3, 4, 2, 1, 7, 5, 6, 3, 4, 2, 1, 8, 9, 5, 6, 3, 4, 2, 1, 9, 12, 9, 5, 6, 3, 4, 2, 1, 10, 7, 12, 9, 5, 6, 3, 4, 2, 1, 11, 14, 19, 12, 9, 5, 6, 3, 4, 2, 1, 12, 13, 17, 19, 16, 9, 5, 6, 3, 4, 2, 1, 13, 8, 7, 17

Offset

1,2

Comments

Is every row a permutation of the natural numbers?

The first row is the positive integers, the second row is A231334, and the main diagonal is A300002.

T(n, m) = A300002(m) for n >= m, thus the rows converge to A300002 in the limit.

Links

Table of n, a(n) for n=1..82.

Example

Table begins
1, 2, 3, 4, 5, 6, 7,  8,  9, 10, 11, 12, 13, 14, 15, 16, ...
1, 2, 4, 3, 6, 5, 9, 12,  7, 14, 13,  8, 23, 17, 18, 22, ...
1, 2, 4, 3, 6, 5, 9, 12, 19, 17,  7,  8, 15, 20, 18, 22, ...
1, 2, 4, 3, 6, 5, 9, 12, 19, 17,  8, 10, 31,  7, 11, 22, ...
1, 2, 4, 3, 6, 5, 9, 16, 14, 20,  7, 15,  8, 12, 18, 31, ...
1, 2, 4, 3, 6, 5, 9, 16, 14, 20,  7, 15,  8, 12, 18, 31, ...
...
In the first row, no two points lie on a 0-degree polynomial (i.e., all terms are distinct).
In the second row, no two terms are the same and no three points (1, a(1)), (2, a(2)), ... lie on the same line.
In the third row, no two terms are the same; no three points (1, a(1)), (2, a(2)), ... lie on the same line; and no four points lie on the same parabola.

Crossrefs

Cf. A231334, A300002.

Sequence in context: A131967 A358120 A329501 * A355474 A137679 A152072

Adjacent sequences: A300667 A300668 A300669 * A300671 A300672 A300673

Keyword

nonn,tabl

Author

Peter Kagey, Mar 11 2018

Status

approved