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Iterate the Kaprekar map of A151949 starting at the n-digit number 100...02; sequence gives the lowest number in the resulting cycle.
5

%I #9 Dec 05 2014 04:52:52

%S 0,495,6174,62964,420876,7509843,64308654,753098643,6431088654,

%T 86420987532,643330866654,8764209875322,64333308666654,

%U 885432098765412,6543331088666544,88543320987665412,975533110888664421

%N Iterate the Kaprekar map of A151949 starting at the n-digit number 100...02; sequence gives the lowest number in the resulting cycle.

%H Joseph Myers, <a href="/A151957/b151957.txt">Table of n, a(n) for n=2..1000</a> [From _Joseph Myers_, Aug 21 2009]

%H <a href="/index/K#Kaprekar_map">Index entries for the Kaprekar map</a>

%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 A151957 := proc(n)

%p local tra,x ;

%p x := 10^(n-1)+2 ;

%p tra := [x] ;

%p while true do

%p x := A151949(x) ;

%p if member(x,tra,'l') then

%p op(l..nops(tra),tra) ;

%p RETURN(min(%)) ;

%p fi;

%p tra := [op(tra),x] :

%p od:

%p end:

%p seq(A151957(n),n=2..60) ;

%p # _R. J. Mathar_, Aug 20 2009

%t To find the first 20 terms of the trajectory of 10002, for instance:

%t f[n_]:=Module[{idn=IntegerDigits[n],idns},idns=Sort[idn];Abs[FromDigits[ idns]-FromDigits[Reverse[idns]]]]

%t NestList[f,10002,20]

%Y See A151958 for the length of the cycles. Cf. A151949, A151955 (the trajectory of 102), A151956 (the trajectory of 1002).

%Y See also A151967, A151968.

%K nonn,base

%O 2,2

%A _Harvey P. Dale_ and _N. J. A. Sloane_, Aug 18 2009, Aug 19 2009

%E Extended by _R. J. Mathar_ and _Joseph Myers_, Aug 20 2009