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A151957 Iterate the Kaprekar map of A151949 starting at the n-digit number 100...02; sequence gives the lowest number in the resulting cycle.

%I A151957 #9 Dec 05 2014 04:52:52
%S A151957 0,495,6174,62964,420876,7509843,64308654,753098643,6431088654,
%T A151957 86420987532,643330866654,8764209875322,64333308666654,
%U A151957 885432098765412,6543331088666544,88543320987665412,975533110888664421
%N A151957 Iterate the Kaprekar map of A151949 starting at the n-digit number 100...02; sequence gives the lowest number in the resulting cycle.
%H A151957 Joseph Myers, <a href="/A151957/b151957.txt">Table of n, a(n) for n=2..1000</a> [From _Joseph Myers_, Aug 21 2009]
%H A151957 <a href="/index/K#Kaprekar_map">Index entries for the Kaprekar map</a>
%p A151957 A151949 := proc(n)
%p A151957 local tup;
%p A151957 tup := sort(convert(n,base,10)) ;
%p A151957 add( (op(i,tup)-op(-i,tup)) *10^(i-1),i=1..nops(tup)) :
%p A151957 end:
%p A151957 A151957 := proc(n)
%p A151957 local tra,x ;
%p A151957 x := 10^(n-1)+2 ;
%p A151957 tra := [x] ;
%p A151957 while true do
%p A151957 x := A151949(x) ;
%p A151957 if member(x,tra,'l') then
%p A151957 op(l..nops(tra),tra) ;
%p A151957 RETURN(min(%)) ;
%p A151957 fi;
%p A151957 tra := [op(tra),x] :
%p A151957 od:
%p A151957 end:
%p A151957 seq(A151957(n),n=2..60) ;
%p A151957 # _R. J. Mathar_, Aug 20 2009
%t A151957 To find the first 20 terms of the trajectory of 10002, for instance:
%t A151957 f[n_]:=Module[{idn=IntegerDigits[n],idns},idns=Sort[idn];Abs[FromDigits[ idns]-FromDigits[Reverse[idns]]]]
%t A151957 NestList[f,10002,20]
%Y A151957 See A151958 for the length of the cycles. Cf. A151949, A151955 (the trajectory of 102), A151956 (the trajectory of 1002).
%Y A151957 See also A151967, A151968.
%K A151957 nonn,base
%O A151957 2,2
%A A151957 _Harvey P. Dale_ and _N. J. A. Sloane_, Aug 18 2009, Aug 19 2009
%E A151957 Extended by _R. J. Mathar_ and _Joseph Myers_, Aug 20 2009