progression.js | jQuery plugin that gives users real time hints | Plugin library

Suppose I have a sequence of increasing numbers, and I want to find the length of longest arithmetic progression within the sequence. Longest arithmetic progression means an increasing sequence with common difference, such as [2, 4, 6, 8] or [3, 6, 9, 12].

For example, for [5, 10, 14, 15, 17], [5, 10, 15] is the longest arithmetic progression, with length 3;

for [10, 12, 13, 20, 22, 23, 30], [10, 20, 30] is the longest arithmetic progression with length 3;

for [7, 10, 12, 13, 15, 20, 21], [10, 15, 20] or [7, 10, 13] are the longest arithmetic progressions with length 3.

This site https://prismoskills.appspot.com/lessons/Dynamic_Programming/Chapter_22_-_Longest_arithmetic_progression.jsp offers some insight into the problem, i.e. by looping around j and consider every 3 elements. I intend to use this algorithm in Python, and my code is as follows: