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A293866 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).

%I A293866 #12 Oct 27 2017 11:07:41
%S A293866 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 A293866 14,15,16,14,15,16,16,17,17,16,17,17,14,15,16,16,17,17,16,17,17,12,13,
%U A293866 14,13,13,14,14,15,16,16,16,16,18,17,24,17,21,21,18,21
%N A293866 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 A293866 The scatterplot of this sequence has interesting features, such as rectangular clusters of points.
%C A293866 For any n > 2, A229037(n) <= a(n) + 1, with equality for n=3, 6, 8, 24 (and possibly no other values).
%H A293866 Rémy Sigrist, <a href="/A293866/b293866.txt">Table of n, a(n) for n = 3..10000</a>
%H A293866 Rémy Sigrist, <a href="/A293866/a293866.png">Scatterplot of the first 100000 terms</a>
%H A293866 Rémy Sigrist, <a href="/A293866/a293866.txt">C++ program for A293866</a>
%F A293866 a(n) = max_{j=1..floor((n-1)/2)} (2*A229037(n-j) - A229037(n-2*j)).
%e A293866 For n=7: A229037(7) must be distinct from:
%e A293866 - 2*A229037(7-1) - A229037(7-2) = 2*2 - 1 = 3,
%e A293866 - 2*A229037(7-2) - A229037(7-4) = 2*1 - 2 = 2,
%e A293866 - 2*A229037(7-3) - A229037(7-6) = 2*1 - 1 = 1.
%e A293866 Hence a(7) = 3.
%o A293866 (C++) See Links section.
%Y A293866 Cf. A229037.
%K A293866 nonn,look
%O A293866 3,2
%A A293866 _Rémy Sigrist_, Oct 18 2017