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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).
3
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, 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, 6, 8, 7, 7, 7, 8, 7, 8, 8, 8, 9, 5, 9, 5, 9, 6, 9, 6, 9
OFFSET
1,6
COMMENTS
Variant of A340488, with XOR(a,y) replaced by ceiling((a+y)/2).
Every number appears, and their first occurrences are in increasing order.
Apparently, a(n) >= A343332(n) for all n.
LINKS
Pontus von Brömssen, Table of n, a(n) for n = 1..10000
PROG
(Python)
def A343333_list(n_max):
a=0
a_list=[0]
count=[]
for i in range(n_max-1):
if a==len(count): count.append(0)
else: count[a]+=1
a=(a+count[a]+1)//2
a_list.append(a)
return a_list
CROSSREFS
KEYWORD
nonn,look
AUTHOR
STATUS
approved