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).

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

Cf. A340488, A343332, A343334.

Sequence in context: A184956 A340134 A218469 * A230502 A280253 A008677

Adjacent sequences: A343330 A343331 A343332 * A343334 A343335 A343336

Keyword

nonn,look

Author

Pontus von Brömssen, Apr 12 2021

Status

approved