A151957 - OEIS

A151957

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

0, 495, 6174, 62964, 420876, 7509843, 64308654, 753098643, 6431088654, 86420987532, 643330866654, 8764209875322, 64333308666654, 885432098765412, 6543331088666544, 88543320987665412, 975533110888664421

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OFFSET

2,2

LINKS

Joseph Myers, Table of n, a(n) for n=2..1000 [From Joseph Myers, Aug 21 2009]

Index entries for the Kaprekar map

MAPLE

A151949 := proc(n)

local tup;

tup := sort(convert(n, base, 10)) ;

add( (op(i, tup)-op(-i, tup)) *10^(i-1), i=1..nops(tup)) :

end:

A151957 := proc(n)

local tra, x ;

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

tra := [x] ;

while true do

x := A151949(x) ;

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

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

RETURN(min(%)) ;

fi;

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

od:

end:

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

# R. J. Mathar, Aug 20 2009

MATHEMATICA

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

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

NestList[f, 10002, 20]

CROSSREFS

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