A343334 - OEIS

%I #10 Apr 15 2021 15:44:31

%S 0,0,1,1,0,2,2,1,1,2,0,3,3,2,1,3,1,4,4,3,0,4,2,2,3,1,5,5,4,1,6,6,5,3,

%T 2,4,0,5,2,5,1,7,7,6,4,1,8,8,7,5,0,6,3,3,4,2,6,2,7,4,3,5,1,9,9,8,6,1,

%U 10,10,9,7,3,6,0,7,2,8,5,2,9,6,1,11,11

%N a(1) = 0; thereafter a(n+1) = abs(a(n)-y), where y is the number of numbers m < n such that a(m) = a(n).

%C Variant of A340488, with XOR(a,y) replaced by abs(a-y).

%C Every number appears, and their first occurrences are in increasing order.

%C Let N_k(n) denote the number of occurrences of k among the first n terms. It appears that N_0(n) ~ sqrt(n/2) and N_k(n) ~ sqrt(2*n) for k > 0.

%H Pontus von Brömssen, <a href="/A343334/b343334.txt">Table of n, a(n) for n = 1..10000</a>

%o (Python)

%o def A343334_list(n_max):

%o   a=0

%o   a_list=[0]

%o   count=[]

%o   for i in range(n_max-1):

%o     if a==len(count): count.append(0)

%o     else: count[a]+=1

%o     a=abs(a-count[a])

%o     a_list.append(a)

%o   return a_list

%Y Cf. A340488, A343332, A343333.

%K nonn,look

%O 1,6

%A _Pontus von Brömssen_, Apr 12 2021