A343333 -id:A343333 - cp's OEIS frontend

A343332 a(1) = 0; thereafter a(n+1) = floor((a(n)+y)/2), where y is the number of numbers m < n such that a(m) = a(n).

0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 1, 3, 1, 3, 2, 2, 2, 3, 2, 3, 3, 3, 4, 2, 4, 2, 4, 3, 4, 3, 5, 2, 5, 3, 5, 3, 6, 3, 6, 3, 7, 3, 7, 4, 4, 4, 5, 4, 5, 4, 6, 4, 6, 4, 7, 4, 7, 5, 5, 5, 6, 5, 6, 5, 7, 5, 7, 6, 6, 6, 7, 6, 7, 7, 7, 8, 4, 8, 4, 8, 5, 8, 5, 8, 6, 8

Offset: 1

Pontus von Brömssen, Apr 12 2021

Variant of A340488, with XOR(a,y) replaced by floor((a+y)/2).
Every number appears, and their first occurrences are in increasing order.
Apparently, a(n) <= A343333(n) for all n.

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Cf. A340488, A343333, A343334.

def A343332_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])//2
    a_list.append(a)
  return a_list

A343334 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).

Original entry on oeis.org

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

Offset: 1

Pontus von Brömssen, Apr 12 2021

Variant of A340488, with XOR(a,y) replaced by abs(a-y).
Every number appears, and their first occurrences are in increasing order.
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.

Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Cf. A340488, A343332, A343333.

def A343334_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=abs(a-count[a])
    a_list.append(a)
  return a_list

cp's OEIS Frontend

A343332 a(1) = 0; thereafter a(n+1) = floor((a(n)+y)/2), where y is the number of numbers m < n such that a(m) = a(n).

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