A151963 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the Kaprekar map in A151949.

1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3, 2, 3, 7, 5, 6, 4, 4, 6, 5, 7, 3

Offset

0,2

Comments

Equals A151962(n) + 1 iff n < 10001 (when a cycle of length greater than 1 occurs for the first time).

Links

Joseph Myers and Robert G. Wilson v, Table of n, a(n) for n = 0..1000 .

Index entries for the Kaprekar map

Example

13->18->63->27->45->9->0->0, so a(13)=6+1 = 7.

Maple

# Maple program from R. J. Mathar:
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:
A151963 := proc(n)
local tra, x ;
tra := [n] ;
x := n ;
while true do
x := A151949(x) ;
if x in tra then
RETURN(nops(tra)) ;
fi;
tra := [op(tra), x] :
od:
end:
seq(A151963(n), n=0..120) ;

Mathematica

f[n_] := Module[{idn = IntegerDigits@n, idns}, idns = Sort@ idn; FromDigits@ Reverse@ idns - FromDigits@ idns]; g[n_] := Length[ NestWhileList[ f, n, UnsameQ, All]] - 1; Table[g@n, {n, 0, 104}] (* Robert G. Wilson v, Aug 20 2009 *)

Crossrefs

In other bases: A164886 (base 2), A164996 (base 3), A165015 (base 4), A165035 (base 5), A165054 (base 6), A165074 (base 7), A165093 (base 8), A165113 (base 9). - Joseph Myers, Sep 05 2009

Sequence in context: A307713 A328680 A256707 * A191291 A131841 A309432

Adjacent sequences: A151960 A151961 A151962 * A151964 A151965 A151966

Keyword

nonn,base

Author

N. J. A. Sloane, Aug 19 2009

Extensions

Typos corrected by Joseph Myers, Aug 20 2009

More terms from R. J. Mathar and Robert G. Wilson v, Aug 20 2009

Status

approved