TSTST 2012 Problem 1

Determine all infinite strings of letters with the following properties: (a) Each letter is either $T$ or $S$, (b) If position $i$ and $j$ both have the letter $T$, then position $i+j$ has the letter $S$, (c) There are infinitely many integers $k$ such that position $2 k-1$ has the $k$ th $T$.