A sequence of integers
is defined as follows:
and for
,
is the smallest integer greater than
such that
for any
and
in
, not necessarily distinct. Determine
.
%V0
A sequence of integers $a_{1},a_{2},a_{3},\ldots$ is defined as follows: $a_{1} = 1$ and for $n\geq 1$, $a_{n + 1}$ is the smallest integer greater than $a_{n}$ such that $a_{i} + a_{j}\neq 3a_{k}$ for any $i,j$ and $k$ in $\{1,2,3,\ldots ,n + 1\}$, not necessarily distinct. Determine $a_{1998}$.
Školjka