[seqfan] Re: The Kaprekar 10% Cascade and A Question

[Hans Havermann]

> For example, while k=4 provides *seven* 4-digit Kaprekars, there are  
> in fact *nine* 4-digit Kaprekars, one provided by the heuristic's  
> k=8 and another by k=9.


I meant of course "one provided by the heuristic's k=5 and another by  
k=6". I've put up an oversized table of *all* my Kaprekar number  
counts from k=1 to k=280 < http://chesswanks.com/num/A194232decomposed.txt 
  >. The sums of the vertical number columns are the entries of  
A194232 (number of n-digit Kaprekar numbers). I have an asterisk  
beside the five k (210, 240, 252, 264, 270) where I do not have actual  
numbers and have substituted in their place estimates based on the  
observation in my previous post. (Feel free to calculate the actuals.)

I'll replace my current a-files for A194232 and A193992 (going up to  
111) with ones going up to 196 (immune, I am assuming, from the  
cascade effect of the still to be calculated k=210). I am currently re- 
doing my k=180 run (it took three weeks) in the hopes of pinning down  
the one-billionth Kaprekar number.