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A308006 Iterate the map x->A308005(x) starting at x=n; a(n) is the number of steps before the first repeated term is encountered.

%I A308006 #10 May 14 2019 08:57:15
%S A308006 3,2,3,2,3,2,3,2,3,2,2,2,2,2,2,2,2,2,2,2,1,2,0,2,1,2,1,2,1,2,2,2,2,1,
%T A308006 2,2,2,2,2,2,1,2,1,2,1,2,1,2,1,2,2,2,2,2,2,2,2,2,2,2,1,2,1,2,1,2,1,2,
%U A308006 1,2,2,2,2,2,2,2,2,2,2,2,1,2,1,2,1
%N A308006 Iterate the map x->A308005(x) starting at x=n; a(n) is the number of steps before the first repeated term is encountered.
%H A308006 Robert Israel, <a href="/A308006/b308006.txt">Table of n, a(n) for n = 0..10000</a>
%e A308006 0 -> 11 -> 220 -> 33 -> 220 -> ... and a number is repeated at step 4, so a(0)=3.
%e A308006 1 -> 110 -> 231 -> 231 -> 231 -> ..., so a(1) = 2.
%e A308006 22 -> 22 -> 22 -> ... is a fixed point, so a(22) = 0.
%p A308006 # using Maple procedure A308006 from that sequence
%p A308006 f:= proc(n) local t,S,i;
%p A308006   S:= {n};
%p A308006   t:= n;
%p A308006   do
%p A308006     t:= A308005(t);
%p A308006     if member(t,S) then return nops(S)-1 fi;
%p A308006     S:= S union {t};
%p A308006   od
%p A308006 end proc:
%p A308006 map(f, [$0..100]); # _Robert Israel_, May 14 2019
%Y A308006 Cf. A308005.
%K A308006 nonn,base
%O A308006 0,1
%A A308006 _N. J. A. Sloane_, May 12 2019