IMO Shortlist 1998 problem N8
Dodao/la:
arhiva2. travnja 2012. Let
![a_{0},a_{1},a_{2},\ldots](/media/m/f/7/9/f79caf5ce3cdfff0460cd7a05feddb74.png)
be an increasing sequence of nonnegative integers such that every nonnegative integer can be expressed uniquely in the form
![a_{i}+2a_{j}+4a_{k}](/media/m/9/0/3/903e7d19bad2d5f3e01b4e3660c94bd5.png)
, where
![i,j](/media/m/6/2/1/621e78d5965ee9a0a0b2a20f342c7f9d.png)
and
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
are not necessarily distinct. Determine
![a_{1998}](/media/m/6/c/2/6c2a1fe46e569b99514799dadb173496.png)
.
%V0
Let $a_{0},a_{1},a_{2},\ldots$ be an increasing sequence of nonnegative integers such that every nonnegative integer can be expressed uniquely in the form $a_{i}+2a_{j}+4a_{k}$, where $i,j$ and $k$ are not necessarily distinct. Determine $a_{1998}$.
Izvor: Međunarodna matematička olimpijada, shortlist 1998