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A329984 a(1) = 0 and for n > 0, a(n+1) is the odd part of k where k is the number of terms equal to a(n) among the first n terms.

%I A329984 #12 Nov 29 2019 12:36:38
%S A329984 0,1,1,1,3,1,1,5,1,3,1,7,1,1,9,1,5,1,11,1,3,3,1,13,1,7,1,15,1,1,17,1,
%T A329984 9,1,19,1,5,3,5,1,21,1,11,1,23,1,3,3,7,3,1,25,1,13,1,27,1,7,1,29,1,15,
%U A329984 1,31,1,1,33,1,17,1,35,1,9,3,9,1,37,1,19,1
%N A329984 a(1) = 0 and for n > 0, a(n+1) is the odd part of k where k is the number of terms equal to a(n) among the first n terms.
%C A329984 In other words, for n > 0, a(n+1) = A000265(o(n)) where o is the ordinal transform of the sequence.
%H A329984 Rémy Sigrist, <a href="/A329984/b329984.txt">Table of n, a(n) for n = 1..10000</a>
%H A329984 Rémy Sigrist, <a href="/A329984/a329984.png">Logarithmic scatterplot of the first 2^16 terms</a>
%e A329984 The first terms, alongside their ordinal transform, are:
%e A329984   n   a(n)  o(n)
%e A329984   --  ----  ----
%e A329984    1     0     1
%e A329984    2     1     1
%e A329984    3     1     2
%e A329984    4     1     3
%e A329984    5     3     1
%e A329984    6     1     4
%e A329984    7     1     5
%e A329984    8     5     1
%e A329984    9     1     6
%e A329984   10     3     2
%o A329984 (PARI) o=vector(38); v=0; for (n=1, 80, print1 (v", "); o[1+v]++; v=o[1+v]/2^valuation(o[1+v],2))
%Y A329984 See A329981 for similar sequences.
%Y A329984 Cf. A000265.
%K A329984 nonn,look
%O A329984 1,5
%A A329984 _Rémy Sigrist_, Nov 26 2019