TxO Math Bowl 2024 - Team Contest - Problem 29

Let a_1, a_2, a_3, \dots, a_n be a sequence satisfying the following properties:

• a_1 = 1
• For each positive integer n > 1, a_n is the smallest positive integer such that there do not exist (not necessarily distinct) positive integers i, j < n with a_i - a_j = a_j - a_n.

Find the sum of the first 24 terms in this sequence.