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A373010 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-2*q, p-q, where q >= 0.

%I A373010 #34 Jun 02 2024 08:21:07
%S A373010 1,1,2,1,1,2,2,3,3,1,1,3,1,1,2,4,3,3,4,3,2,2,4,4,2,2,5,1,1,3,1,1,2,4,
%T A373010 4,5,1,1,3,1,1,5,4,5,3,6,5,6,5,4,6,6,4,3,4,3,3,4,3,6,2,6,5,7,3,6,6,3,
%U A373010 2,7,6,7,5,5,2,2,6,2,2,4,5,1,1,2,1,1,5,2,6,7
%N A373010 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-2*q, p-q, where q >= 0.
%C A373010 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 (3,1,2) and other progressions of the form p, p-2*q, p-q, for all q >= 0.
%H A373010 Neal Gersh Tolunsky, <a href="/A373010/b373010.txt">Table of n, a(n) for n = 1..10000</a>
%H A373010 Neal Gersh Tolunsky, <a href="/A373010/a373010.png">Graph of first 200000 terms</a>.
%F A373010 a(n)=1 iff n in A003278.
%Y A373010 Cf. A229037, A100480, A309890, A373052, A373111, A361933, A371632.
%K A373010 nonn
%O A373010 1,3
%A A373010 _Neal Gersh Tolunsky_, May 22 2024