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%I #13 Nov 29 2019 12:15:52
%S 0,1,1,2,1,2,2,3,1,1,2,3,2,3,3,4,1,1,2,2,3,4,2,3,4,3,4,4,5,1,0,-6,1,1,
%T 2,2,3,3,4,5,2,2,3,4,5,3,4,5,4,5,5,6,1,-1,-1,0,-8,1,0,-8,2,2,3,3,4,4,
%U 5,6,2,2,3,3,4,5,6,3,4,5,6,4,5,6,5,6,6
%N a(1) = 0, and for n > 0, a(n+1) = u - v where u (resp. v) is the number of terms equal to a(n) (resp. a(n)+1) among the first n terms.
%C The sequence has chaotic features (see plot in Links section).
%H Rémy Sigrist, <a href="/A330004/b330004.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A330004/a330004.png">Density plot of the first 25000000 terms</a>
%e The first terms, alongside u and v, are:
%e n a(n) u v
%e -- ---- - -
%e 1 0 1 0
%e 2 1 1 0
%e 3 1 2 0
%e 4 2 1 0
%e 5 1 3 1
%e 6 2 2 0
%e 7 2 3 0
%e 8 3 1 0
%e 9 1 4 3
%e 10 1 5 3
%o (PARI) for (n=1, #(a=vector(85)), print1 (a[n]=if (n==1, 0, sum(k=1, n-1, (a[k]==a[n-1])-(a[k]==a[n-1]+1)))", "))
%Y See A329981 for similar sequences.
%K sign,look
%O 1,4
%A _Rémy Sigrist_, Nov 26 2019
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