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A371632 Lexicographically earliest sequence of positive integers such that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form a progression of the form p, p+q, p-q, where q >= 0.

%I A371632 #21 Jun 01 2024 06:20:43
%S A371632 1,1,2,1,1,2,2,3,3,2,3,2,4,1,3,2,1,3,2,3,4,1,2,3,4,3,4,4,5,4,1,5,5,4,
%T A371632 1,4,2,5,5,6,5,5,6,6,7,7,3,7,6,6,8,6,6,5,7,7,8,7,1,8,8,9,9,8,5,3,9,9,
%U A371632 10,9,6,8,8,5,9,9,5,8,6,10,1,7,10,6,6,4,4,8,3,10
%N A371632 Lexicographically earliest sequence of positive integers such that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form a progression of the form p, p+q, p-q, where q >= 0.
%C A371632 This sequence avoids one of the six permutations of a set of three integers in arithmetic progression. For example, the set {1,2,3} can be ordered as tuples (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). In this sequence, we avoid (2,3,1) and other progressions of the form p, p+q, p-q, for all q >= 0.
%H A371632 Neal Gersh Tolunsky, <a href="/A371632/b371632.txt">Table of n, a(n) for n = 1..10000</a>
%H A371632 Neal Gersh Tolunsky, <a href="/A371632/a371632.png">Graph of first 200000 terms</a>.
%Y A371632 Cf. A229037, A100480, A373010, A309890, A373052, A373111, A361933.
%K A371632 nonn
%O A371632 1,3
%A A371632 _Neal Gersh Tolunsky_, May 24 2024