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A343333 a(1) = 0; thereafter a(n+1) = ceiling((a(n)+y)/2), where y is the number of numbers m < n such that a(m) = a(n).

%I A343333 #11 Apr 16 2021 00:05:16
%S A343333 0,0,1,1,1,2,1,2,2,2,3,2,3,2,4,2,4,3,3,3,4,3,4,4,4,5,3,5,3,5,4,5,4,6,
%T A343333 3,6,4,6,4,7,4,7,4,8,4,8,5,5,5,6,5,6,5,7,5,7,5,8,5,8,6,6,6,7,6,7,6,8,
%U A343333 6,8,7,7,7,8,7,8,8,8,9,5,9,5,9,6,9,6,9
%N A343333 a(1) = 0; thereafter a(n+1) = ceiling((a(n)+y)/2), where y is the number of numbers m < n such that a(m) = a(n).
%C A343333 Variant of A340488, with XOR(a,y) replaced by ceiling((a+y)/2).
%C A343333 Every number appears, and their first occurrences are in increasing order.
%C A343333 Apparently, a(n) >= A343332(n) for all n.
%H A343333 Pontus von Brömssen, <a href="/A343333/b343333.txt">Table of n, a(n) for n = 1..10000</a>
%o A343333 (Python)
%o A343333 def A343333_list(n_max):
%o A343333   a=0
%o A343333   a_list=[0]
%o A343333   count=[]
%o A343333   for i in range(n_max-1):
%o A343333     if a==len(count): count.append(0)
%o A343333     else: count[a]+=1
%o A343333     a=(a+count[a]+1)//2
%o A343333     a_list.append(a)
%o A343333   return a_list
%Y A343333 Cf. A340488, A343332, A343334.
%K A343333 nonn,look
%O A343333 1,6
%A A343333 _Pontus von Brömssen_, Apr 12 2021