A151962 Length of preperiodic part of trajectory of n under iteration of the Kaprekar map in A151949.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2, 1, 2, 6, 4, 5, 3, 3, 5, 4, 6, 2

Offset: 0

Author

N. J. A. Sloane, Aug 19 2009

Keywords

• nonn
• base

Examples

			13 -> 18 -> 63 -> 27 -> 45 -> 9 -> 0 -> 0, so a(13)=6.
		

Links

• Joseph Myers, Table of n, a(n) for n = 0..1000
• Index entries for the Kaprekar map

Crossrefs

Cf. A151949, A151963. Strictly different from A072137.

In other bases: A164885 (base 2), A164995 (base 3), A165014 (base 4), A165034 (base 5), A165053 (base 6), A165073 (base 7), A165092 (base 8), A165112 (base 9). - Joseph Myers, Sep 05 2009

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:
A151962 := proc(n)
local tra,x ;
tra := [n] ;
x := n ;
while true do
x := A151949(x) ;
if member(x,tra,'l') then
RETURN(l-1) ;
fi;
tra := [op(tra),x] :
od:
end:
seq(A151962(n),n=0..120) ;
# R. J. Mathar, Aug 20 2009

Extensions

More terms from R. J. Mathar, Aug 20 2009