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

Offset: 2

Author

Harvey P. Dale and N. J. A. Sloane, Aug 18 2009, Aug 19 2009

Keywords

• nonn
• base

Links

• Joseph Myers, Table of n, a(n) for n=2..1000 [From _Joseph Myers_, Aug 21 2009]
• Index entries for the Kaprekar map

Crossrefs

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

See also A151967, A151968.

Programs

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]

Extensions

Extended by R. J. Mathar and Joseph Myers, Aug 20 2009