Question 74
Find all infinite sequences $a_1, a_2, \dots$ of positive integers satisfying the following properties:
a. $a_1 \lt a_2 \lt a_3 \lt \dots$,
b. there are no positive integers $i, j, k$, not necessarily distinct, such that $a_i + a_j = a_k$,
c. there are infinitely many positive integers $k$ such that $a_k = 2k - 1$.
a. $a_1 \lt a_2 \lt a_3 \lt \dots$,
b. there are no positive integers $i, j, k$, not necessarily distinct, such that $a_i + a_j = a_k$,
c. there are infinitely many positive integers $k$ such that $a_k = 2k - 1$.