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%I #9 Mar 16 2019 02:24:45
%S 0,1,1,1,1,1,1,1,1,1,2,1,2,6,4,5,3,3,5,4,6,2,1,2,6,4,5,3,3,5,4,6,2,1,
%T 2,6,4,5,3,3,5,4,6,2,1,2,6,4,5,3,3,5,4,6,2,1,2,6,4,5,3,3,5,4,6,2,1,2,
%U 6,4,5,3,3,5,4,6,2,1,2,6,4,5,3,3,5,4,6,2,1,2,6,4,5,3,3,5,4,6,2
%N Length of preperiodic part of trajectory of n under iteration of the Kaprekar map in A151949.
%H Joseph Myers, <a href="/A151962/b151962.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/K#Kaprekar_map">Index entries for the Kaprekar map</a>
%e 13 -> 18 -> 63 -> 27 -> 45 -> 9 -> 0 -> 0, so a(13)=6.
%p A151949 := proc(n)
%p local tup;
%p tup := sort(convert(n,base,10)) ;
%p add( (op(i,tup)-op(-i,tup)) *10^(i-1),i=1..nops(tup)) :
%p end:
%p A151962 := proc(n)
%p local tra,x ;
%p tra := [n] ;
%p x := n ;
%p while true do
%p x := A151949(x) ;
%p if member(x,tra,'l') then
%p RETURN(l-1) ;
%p fi;
%p tra := [op(tra),x] :
%p od:
%p end:
%p seq(A151962(n),n=0..120) ;
%p # _R. J. Mathar_, Aug 20 2009
%Y Cf. A151949, A151963. Strictly different from A072137.
%Y In other bases: A164885 (base 2), A164995 (base 3), A165014 (base 4), A165034 (base 5), A165053 (base 6), A165073 (base 7), A165092 (base 8), A165112 (base 9). - _Joseph Myers_, Sep 05 2009
%K nonn,base
%O 0,11
%A _N. J. A. Sloane_, Aug 19 2009
%E More terms from _R. J. Mathar_, Aug 20 2009
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