Arithmetic progression

def arithmetic_progression(items):

An arithmetic progression is a numerical sequence so that the stride between each two consecutive elements is constant throughout the sequence. For example, [4, 8, 12, 16, 20] is an arithmetic progression of length 5, starting from the value 4 with a stride of 4.

Given a non-empty list items of positive integers in strictly ascending order, find and return the longest arithmetic progression whose all values exist somewhere in that sequence. Return the answer as a tuple (start, stride, n) of the values that define the progression. To ensure unique results to facilitate automated testing, if there exist several progressions of the same length, this function should return the one with the lowest start. If several progressions of equal length emanate from the lowest start, return the progression with the smallest stride.

(Bridge players like to distinguish between "best result possible" and "best possible result", which are not at all the same thing. In the same spirit, can you see the difference between two deceptively similar concepts of "leftmost of longest" and "longest of leftmost" in this problem?)

items Expected result

[42] (42, 0, 1)

[2, 4, 6, 7, 8, 12, 17] (2, 2, 4)

[1, 2, 36, 49, 50, 70, 75, 98, 104, 138, 146, 148, 172, 206, 221, 240, 274, 294, 367, 440] (2, 34, 9)

[2, 3, 7, 20, 25, 26, 28, 30, 32, 34, 36, 41, 53, 57, 73, 89, 94, 103, 105, 121, 137, 181, 186, 268, 278, 355, 370, 442, 462, 529, 554, 616, 646, 703] (7, 87, 9) range(1000000) (0, 1, 1000000)