May 2021 - Solution
As many have pointed out, this problem was originally solved by Ronald Graham who found a specific set of triplets ( "A Fibonacci-like sequence of composite numbers" , also given in the excellent book "Concrete mathematics"). The challenge here was not copying the set from the paper!
Alternative sets can also be given, such as
s = [[2, 3, 3], [3, 4, 4], [5, 5, 5], [7, 8, 1], [17, 9, 1], [11, 10, 1], [61, 15, 2], [47, 16, 2], [19, 18, 7], [41, 20, 3], [23, 24, 14], [31, 30, 29], [2207, 32, 10], [107, 36, 22], [2161, 40, 13], [109441, 45, 4], [1103, 48, 26], [103681, 72, 70], [181, 90, 67], [769, 96, 58]]
Yielding
A0 = 44186851375096125029100906489607183486440
A1 = 23990976680675392254644252020033167422281