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%I #12 Apr 27 2018 17:14:51
%S 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,
%T 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,
%U 1,12,13,17,19,16,9,5,6,3,4,2,1,13,8,7,17
%N 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.
%C Is every row a permutation of the natural numbers?
%C The first row is the positive integers, the second row is A231334, and the main diagonal is A300002.
%C T(n, m) = A300002(m) for n >= m, thus the rows converge to A300002 in the limit.
%e Table begins
%e 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, ...
%e 1, 2, 4, 3, 6, 5, 9, 12, 7, 14, 13, 8, 23, 17, 18, 22, ...
%e 1, 2, 4, 3, 6, 5, 9, 12, 19, 17, 7, 8, 15, 20, 18, 22, ...
%e 1, 2, 4, 3, 6, 5, 9, 12, 19, 17, 8, 10, 31, 7, 11, 22, ...
%e 1, 2, 4, 3, 6, 5, 9, 16, 14, 20, 7, 15, 8, 12, 18, 31, ...
%e 1, 2, 4, 3, 6, 5, 9, 16, 14, 20, 7, 15, 8, 12, 18, 31, ...
%e ...
%e In the first row, no two points lie on a 0-degree polynomial (i.e., all terms are distinct).
%e 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.
%e 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.
%Y Cf. A231334, A300002.
%K nonn,tabl
%O 1,2
%A _Peter Kagey_, Mar 11 2018
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