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