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%I #19 Nov 04 2023 21:52:46
%S 1,1,2,1,4,6,2,9,1,13,8,19,2,15,12,28,32,6,4,18,43,1,51,16,36,41,28,
%T 34,2,57,66,10,80,5,31,24,61,71,89,12,107,128,18,99,42,1,123,142,10,
%U 38,78,164,120,21,1,58,183,169,99,93,203,22,200,155,7,130,228
%N Lexicographically earliest sequence of positive integers such that no two distinct unordered pairs of points ((n, a(n)), (m, a(m))) and ((k, a(k)), (j, a(j))) have the same midpoint.
%C No three terms a(j), a(j+k), a(j+2k) (for any j and k) form an arithmetic progression.
%H Giovanni Resta, <a href="/A285491/b285491.txt">Table of n, a(n) for n = 1..4000</a> (first 650 terms from Peter Kagey)
%e For n = 3:
%e a(3) != 1 or else midpoint((1, 1), (3, 1)) = midpoint((2, 1), (2, 1)), so
%e a(3) = 2.
%e For n = 5:
%e a(5) != 1 or else midpoint((1, 1), (5, 1)) = midpoint((2, 1), (4, 1));
%e a(5) != 2 or else midpoint((2, 1), (5, 2)) = midpoint((3, 2), (4, 1));
%e a(5) != 3 or else midpoint((1, 1), (5, 3)) = midpoint((3, 2), (3, 2)); so
%e a(5) = 4.
%Y Cf. A229037, A248625, A285490.
%K nonn,look
%O 1,3
%A _Peter Kagey_, Apr 19 2017
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