proposed

approved

editing

proposed

Maple program from R. J. Mathar, Aug 20 2009

# R. J. Mathar, Aug 20 2009

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

approved

editing

_Harvey P. Dale (hpd1(AT)nyu.edu) _ and N. J. A. Sloane, Aug 18 2009, Aug 19 2009

Joseph Myers, <a href="/A151957/b151957.txt">Table of n, a(n) for n=2..1000</a> [From _Joseph Myers (jsm(AT)polyomino.org.uk), _, Aug 21 2009]

Extended by R. J. Mathar and _Joseph Myers (jsm(AT)polyomino.org.uk), _, Aug 20 2009

Harvey P. Dale (hpd1(AT)nyu.edu) and _N. J. A. Sloane (njas(AT)research.att.com), _, Aug 18 2009, Aug 19 2009

<a href="/Sindx_index/K.html#Kaprekar_map">Index entries for the Kaprekar map</a>

Joseph Myers, <a href="/A151957/b151957.txt">Table of n, a(n) for n=2..1000</a> [From Joseph Myers (jsm(AT)polyomino.org.uk), Aug 21 2009]

<a href="/Sindx_K.html#Kaprekar_map">Index entries for the Kaprekar map</a>

nonn,base,new

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

2,2

Joseph Myers, <a href="b151957.txt">Table of n, a(n) for n=2..1000</a> [From Joseph Myers (jsm(AT)polyomino.org.uk), Aug 21 2009]

<a href="Sindx_K.html#Kaprekar_map">Index entries for the Kaprekar map</a>

Maple program from R. J. Mathar, Aug 20 2009

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) ;

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]

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

See also A151967, A151968.

nonn,base

Harvey P. Dale (hpd1(AT)nyu.edu) and N. J. A. Sloane (njas(AT)research.att.com), Aug 18 2009, Aug 19 2009

Extended by R. J. Mathar and Joseph Myers (jsm(AT)polyomino.org.uk), Aug 20 2009

approved