A151956 -id:A151956 - cp's OEIS frontend

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

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

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

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

See also A151967, A151968.

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

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]

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

A151946 a(1) = 8127; thereafter a(n) = (a(n-1) with digits sorted into descending order) - (a(n-1) with digits sorted into ascending order) (see the Kaprekar map, A151949).

Original entry on oeis.org

8127, 7443, 3996, 6264, 4176, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174, 6174

Offset: 1

N. J. A. Sloane, Aug 18 2009

Similar in spirit to the RATS (Reverse, Add Then Sort) sequences.
Converges to the fixed point 6174. For the list of fixed points see A099009.
The initial value 1001 is the smallest number that converges to 6174 - see A151967.

Cf. A099009, A151947, A151949, A151951, A151955, A151956, A151967. A151968.

cp's OEIS Frontend

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

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