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A293862 Sequence of signed integers where each is chosen to be as small as possible (in absolute value) subject to the condition that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form an arithmetic progression; in case of a tie, preference is given to the positive value.

%I A293862 #16 Oct 27 2017 11:09:21
%S A293862 0,0,1,0,0,1,1,-1,-1,0,0,-1,0,0,1,3,3,-1,3,3,1,1,2,2,1,-3,2,0,0,-2,0,
%T A293862 0,1,-3,-3,-2,0,0,4,0,0,1,-2,-1,-1,-2,5,-1,3,-3,2,3,3,2,5,4,4,2,4,2,3,
%U A293862 -1,-1,3,-8,-2,5,2,-2,-2,-8,-3,-2,-8,-6,-6,2,5
%N A293862 Sequence of signed integers where each is chosen to be as small as possible (in absolute value) subject to the condition that no three terms a(j), a(j+k), a(j+2k) (for any j and k) form an arithmetic progression; in case of a tie, preference is given to the positive value.
%C A293862 This sequence is a "signed" variant of A229037. Graphically, both sequences have similar ethereal features.
%C A293862 For any n > 0, |a(n)| <= floor( (n+1)/4 ).
%H A293862 Rémy Sigrist, <a href="/A293862/b293862.txt">Table of n, a(n) for n = 1..100000</a>
%H A293862 Rémy Sigrist, <a href="/A293862/a293862.png">Scatterplot of the first 1000000 terms</a>
%H A293862 Rémy Sigrist, <a href="/A293862/a293862_1.txt">C++ program for A293862</a>
%e A293862 a(1) = 0 is suitable.
%e A293862 a(2) = 0 is suitable.
%e A293862 a(3) cannot equal 0 as 2*a(3-1) - a(3-2) = 0.
%e A293862 a(3) = 1 is suitable.
%e A293862 a(4) cannot equal 2 as 2*a(4-1) - a(4-2) = 2.
%e A293862 a(4) = 0 is suitable.
%e A293862 a(5) cannot equal -1 as 2*a(5-1) - a(5-2) = -1.
%e A293862 a(5) cannot equal 2 as 2*a(5-2) - a(5-4) = 2.
%e A293862 a(5) = 0 is suitable.
%e A293862 a(6) cannot equal 0 as 2*a(6-1) - a(6-2) = 0.
%e A293862 a(6) = 1 is suitable.
%e A293862 a(7) cannot equal 2 as 2*a(7-1) - a(7-2) = 2.
%e A293862 a(7) cannot equal -1 as 2*a(7-2) - a(7-4) = -1.
%e A293862 a(7) cannot equal 0 as 2*a(7-3) - a(7-6) = 0.
%e A293862 a(7) = 1 is suitable.
%e A293862 a(8) cannot equal 1 as 2*a(8-1) - a(8-2) = 1.
%e A293862 a(8) cannot equal 2 as 2*a(8-2) - a(8-4) = 2.
%e A293862 a(8) cannot equal 0 as 2*a(8-3) - a(8-6) = 0.
%e A293862 a(8) = -1 is suitable.
%o A293862 (C++) See Links section.
%K A293862 sign
%O A293862 1,16
%A A293862 _Rémy Sigrist_, Oct 18 2017