A354254 a(n) is the least m >= 0 such that n = f^k(m) for some k >= 0 (where f^k denotes the k-th iterate of A092391).

0, 1, 1, 1, 4, 1, 6, 1, 6, 6, 1, 6, 1, 13, 1, 15, 13, 1, 18, 1, 18, 21, 1, 23, 21, 1, 21, 23, 1, 21, 30, 1, 32, 21, 30, 21, 1, 37, 1, 39, 37, 1, 37, 39, 1, 37, 46, 1, 48, 37, 46, 51, 1, 46, 54, 1, 56, 46, 54, 56, 1, 46, 54, 63, 1, 1, 46, 1, 46, 63, 1, 71, 63

Offset: 0

Author

Rémy Sigrist, May 21 2022

Keywords

• nonn
• base

Examples

			The first terms, alongside f(n), are:
  n   a(n)  f(n)
  --  ----  ----
   0     0     0
   1     1     2
   2     1     3
   3     1     5
   4     4     5
   5     1     7
   6     6     8
   7     1    10
   8     6     9
   9     6    11
  10     1    12
  11     6    14
  12     1    14
  13    13    16
  14     1    17
		

Crossrefs

Cf. A010061, A010062, A092391, A179016.

Programs

PARI

a = vector(73, n, n-1); for (n=0, #a-1, m=n+hammingweight(n); if (m<#a, a[1+m]=min(a[1+n],a[1+m]))); print (a)

Formula

a(n) = n iff n = 0 or n belongs to A010061.

a(n) = 1 iff n belongs to A010062.