A354254 - OEIS

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 #5 May 27 2022 14:37:25

%S 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 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 54,1,56,46,54,56,1,46,54,63,1,1,46,1,46,63,1,71,63

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

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

%e The first terms, alongside f(n), are:

%e n a(n) f(n)

%e -- ---- ----

%e 0 0 0

%e 1 1 2

%e 2 1 3

%e 3 1 5

%e 4 4 5

%e 5 1 7

%e 6 6 8

%e 7 1 10

%e 8 6 9

%e 9 6 11

%e 10 1 12

%e 11 6 14

%e 12 1 14

%e 13 13 16

%e 14 1 17

%o (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 Cf. A010061, A010062, A092391, A179016.

%K nonn,base

%O 0,5

%A _Rémy Sigrist_, May 21 2022