Question 29
Does there exist an increasing sequence of integers $0 = a_0 \lt a_1 \lt a_2 \lt \dots$, such that the following two conditions are satisfied:
1) every natural number can be written in the form $a_i + a_j$ for some (maybe equal) indices $i, j \ge 0$;
2) $a_n \gt \frac{n^2}{16}$ for all natural $n$?
1) every natural number can be written in the form $a_i + a_j$ for some (maybe equal) indices $i, j \ge 0$;
2) $a_n \gt \frac{n^2}{16}$ for all natural $n$?