1994 OIM Problems/Problem 6
Problem
Show that every natural number 
can be obtained after 1 by doing less than 1,100,000 additions; more precisely, there is a finite sequence of natural numbers
![\[x_0, x_1, \cdots , x_k \; \text{with }\; k \le 1,100,000,\; x_0=1,\; x_k=n,\]](http://latex.artofproblemsolving.com/a/7/e/a7e93684163d173bf7ca9c971278a06750d0b5b4.png)
such that for each 
, there exist 
, 
, with 
, 
, 
, and 
.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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