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A373111 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 c, c+2d, c+d, where d >= 0.

%I A373111 #16 Jun 09 2024 07:30:40
%S A373111 1,1,2,1,1,2,2,3,3,1,1,3,1,1,4,4,3,2,3,3,4,4,5,4,4,5,5,1,1,4,1,1,5,5,
%T A373111 6,5,1,1,6,1,1,2,2,5,2,2,5,6,6,7,2,2,7,2,2,8,7,6,5,6,8,8,9,5,6,9,8,9,
%U A373111 2,2,7,3,2,8,2,3,8,7,3,7,4,1,1,6,1,1,9,8
%N A373111 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 c, c+2d, c+d, where d >= 0.
%C A373111 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 (1,3,2) and other progressions of the form c, c+2d, c+d, for all d >= 0.
%H A373111 Neal Gersh Tolunsky, <a href="/A373111/b373111.txt">Table of n, a(n) for n = 1..10000</a>
%H A373111 Neal Gersh Tolunsky, <a href="/A373111/a373111.png">Graph of first 200000 terms</a>.
%F A373111 a(n)=1 iff n in A003278.
%Y A373111 Cf. A229037, A373010, A100480, A309890, A373052, A361933, A371632, A371457.
%K A373111 nonn
%O A373111 1,3
%A A373111 _Neal Gersh Tolunsky_, May 25 2024