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A151963 (Length of preperiodic part) + (length of cycle) of trajectory of n under iteration of the Kaprekar map in A151949. 10

%I

%S 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,

%T 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,

%U 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

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

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

%H Joseph Myers and Robert G. Wilson v, <a href="/A151963/b151963.txt">Table of n, a(n) for n = 0..1000 </a>.

%H <a href="/index/K#Kaprekar_map">Index entries for the Kaprekar map</a>

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

%p # Maple program from _R. J. Mathar_:

%p A151949 := proc(n)

%p local tup;

%p tup := sort(convert(n,base,10)) ;

%p add( (op(i,tup)-op(-i,tup)) *10^(i-1),i=1..nops(tup)) :

%p end:

%p A151963 := proc(n)

%p local tra,x ;

%p tra := [n] ;

%p x := n ;

%p while true do

%p x := A151949(x) ;

%p if x in tra then

%p RETURN(nops(tra)) ;

%p fi;

%p tra := [op(tra),x] :

%p od:

%p end:

%p seq(A151963(n),n=0..120) ;

%t 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 *)

%Y 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

%K nonn,base

%O 0,2

%A _N. J. A. Sloane_, Aug 19 2009

%E Typos corrected by _Joseph Myers_, Aug 20 2009

%E More terms from _R. J. Mathar_ and _Robert G. Wilson v_, Aug 20 2009

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Last modified August 16 00:25 EDT 2018. Contains 313782 sequences. (Running on oeis4.)