cp's OEIS Frontend

A285491 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.

%I A285491 #19 Nov 04 2023 21:52:46
%S A285491 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 A285491 34,2,57,66,10,80,5,31,24,61,71,89,12,107,128,18,99,42,1,123,142,10,
%U A285491 38,78,164,120,21,1,58,183,169,99,93,203,22,200,155,7,130,228
%N A285491 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 A285491 No three terms a(j), a(j+k), a(j+2k) (for any j and k) form an arithmetic progression.
%H A285491 Giovanni Resta, <a href="/A285491/b285491.txt">Table of n, a(n) for n = 1..4000</a> (first 650 terms from Peter Kagey)
%e A285491 For n = 3:
%e A285491 a(3) != 1 or else midpoint((1, 1), (3, 1)) = midpoint((2, 1), (2, 1)), so
%e A285491 a(3) = 2.
%e A285491 For n = 5:
%e A285491 a(5) != 1 or else midpoint((1, 1), (5, 1)) = midpoint((2, 1), (4, 1));
%e A285491 a(5) != 2 or else midpoint((2, 1), (5, 2)) = midpoint((3, 2), (4, 1));
%e A285491 a(5) != 3 or else midpoint((1, 1), (5, 3)) = midpoint((3, 2), (3, 2)); so
%e A285491 a(5) = 4.
%Y A285491 Cf. A229037, A248625, A285490.
%K A285491 nonn,look
%O A285491 1,3
%A A285491 _Peter Kagey_, Apr 19 2017