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A330004 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.

%I A330004 #13 Nov 29 2019 12:15:52
%S A330004 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 A330004 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 A330004 5,6,2,2,3,3,4,5,6,3,4,5,6,4,5,6,5,6,6
%N A330004 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 A330004 The sequence has chaotic features (see plot in Links section).
%H A330004 Rémy Sigrist, <a href="/A330004/b330004.txt">Table of n, a(n) for n = 1..10000</a>
%H A330004 Rémy Sigrist, <a href="/A330004/a330004.png">Density plot of the first 25000000 terms</a>
%e A330004 The first terms, alongside u and v, are:
%e A330004   n   a(n)  u  v
%e A330004   --  ----  -  -
%e A330004    1     0  1  0
%e A330004    2     1  1  0
%e A330004    3     1  2  0
%e A330004    4     2  1  0
%e A330004    5     1  3  1
%e A330004    6     2  2  0
%e A330004    7     2  3  0
%e A330004    8     3  1  0
%e A330004    9     1  4  3
%e A330004   10     1  5  3
%o A330004 (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 A330004 See A329981 for similar sequences.
%K A330004 sign,look
%O A330004 1,4
%A A330004 _Rémy Sigrist_, Nov 26 2019