2022 AIME I Problem 6

Find the number of ordered pairs of integers (a,b) such that the sequence 3,4,5,a,b,30,40,50 is strictly increasing and no set of four (not necessarily consecutive) terms forms an arithmetic progression.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.