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For n > 2: when computing A229037(n), there are up to floor((n-1)/2) forbidden values (i.e. values that would lead to an arithmetic progression); a(n) = greatest forbidden value when computing A229037(n).
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%I #12 Oct 27 2017 11:07:41

%S 1,3,3,1,3,3,6,6,7,7,7,7,7,7,7,6,6,7,7,7,7,7,11,11,12,13,14,12,13,14,

%T 14,15,16,14,15,16,16,17,17,16,17,17,14,15,16,16,17,17,16,17,17,12,13,

%U 14,13,13,14,14,15,16,16,16,16,18,17,24,17,21,21,18,21

%N For n > 2: when computing A229037(n), there are up to floor((n-1)/2) forbidden values (i.e. values that would lead to an arithmetic progression); a(n) = greatest forbidden value when computing A229037(n).

%C The scatterplot of this sequence has interesting features, such as rectangular clusters of points.

%C For any n > 2, A229037(n) <= a(n) + 1, with equality for n=3, 6, 8, 24 (and possibly no other values).

%H Rémy Sigrist, <a href="/A293866/b293866.txt">Table of n, a(n) for n = 3..10000</a>

%H Rémy Sigrist, <a href="/A293866/a293866.png">Scatterplot of the first 100000 terms</a>

%H Rémy Sigrist, <a href="/A293866/a293866.txt">C++ program for A293866</a>

%F a(n) = max_{j=1..floor((n-1)/2)} (2*A229037(n-j) - A229037(n-2*j)).

%e For n=7: A229037(7) must be distinct from:

%e - 2*A229037(7-1) - A229037(7-2) = 2*2 - 1 = 3,

%e - 2*A229037(7-2) - A229037(7-4) = 2*1 - 2 = 2,

%e - 2*A229037(7-3) - A229037(7-6) = 2*1 - 1 = 1.

%e Hence a(7) = 3.

%o (C++) See Links section.

%Y Cf. A229037.

%K nonn,look

%O 3,2

%A _Rémy Sigrist_, Oct 18 2017