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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).

%I A354254 #5 May 27 2022 14:37:25
%S A354254 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,
%T A354254 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,
%U A354254 54,1,56,46,54,56,1,46,54,63,1,1,46,1,46,63,1,71,63
%N 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).
%F A354254 a(n) = n iff n = 0 or n belongs to A010061.
%F A354254 a(n) = 1 iff n belongs to A010062.
%e A354254 The first terms, alongside f(n), are:
%e A354254   n   a(n)  f(n)
%e A354254   --  ----  ----
%e A354254    0     0     0
%e A354254    1     1     2
%e A354254    2     1     3
%e A354254    3     1     5
%e A354254    4     4     5
%e A354254    5     1     7
%e A354254    6     6     8
%e A354254    7     1    10
%e A354254    8     6     9
%e A354254    9     6    11
%e A354254   10     1    12
%e A354254   11     6    14
%e A354254   12     1    14
%e A354254   13    13    16
%e A354254   14     1    17
%o A354254 (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)
%Y A354254 Cf. A010061, A010062, A092391, A179016.
%K A354254 nonn,base
%O A354254 0,5
%A A354254 _Rémy Sigrist_, May 21 2022