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A381629 Lexicographically earliest sequence of positive integers such that no subsequence of terms at indices in arithmetic progression form an arithmetic progression in any order.

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%I A381629 #38 May 07 2025 10:41:06
%S A381629 1,1,2,1,1,2,2,4,4,1,1,2,1,1,2,2,4,4,2,4,4,5,5,8,5,5,9,9,4,2,5,11,2,2,
%T A381629 4,1,1,5,1,1,10,2,2,4,1,1,4,4,10,10,4,10,10,12,2,4,1,2,5,4,5,10,4,2,8,
%U A381629 2,10,5,5,10,5,13,12,13,2,5,10,5,10,10,13,5
%N A381629 Lexicographically earliest sequence of positive integers such that no subsequence of terms at indices in arithmetic progression form an arithmetic progression in any order.
%C A381629 First differs from A361933 at a(52).
%C A381629 This is a variant of A361933 generalized to arithmetic progressions of any nontrivial length (3 or greater).
%H A381629 Neal Gersh Tolunsky, <a href="/A381629/b381629.txt">Table of n, a(n) for n = 1..1000</a>
%e A381629 a(52) cannot be values 1-7 without creating an arithmetic progression. a(52) cannot be 8 because the terms at i = 22,32,42,52 (common difference 10) would have the terms 5,11,2,8, which, rearranged, form the progression 2,5,8,11 (common difference 3). a(52) cannot be 9 because the terms at i = 38,45,52 (common difference 7) would have the terms 5,1,9, which in the order 1,5,9 form an arithmetic progression (common difference 4). So a(52) = 10.
%Y A381629 Cf. A361933.
%K A381629 nonn
%O A381629 1,3
%A A381629 _Neal Gersh Tolunsky_, Mar 29 2025