Discover long patterns

Question

Given a sorted list of numbers, I would like to find the longest subsequence where the differences between successive elements are geometrically increasing. So if the list is <

Answer 1

Python:

def subseq(a):
    seq = []
    aset = set(a)
    for i, x in enumerate(a):
        # elements after x
        for j, x2 in enumerate(a[i+1:]):
            j += i + 1  # enumerate starts j at 0, we want a[j] = x2
            bk = x2 - x  # b*k (assuming k and k's exponent start at 1)

            # given b*k, bruteforce values of k
            for k in range(1, bk + 1):
                items = [x, x2]  # our subsequence so far
                nextdist = bk * k # what x3 - x2 should look like

                while items[-1] + nextdist in aset:
                    items.append(items[-1] + nextdist)
                    nextdist *= k

                if len(items) > len(seq):
                    seq = items

    return seq

Running time is O(dn^3), where d is the (average?) distance between two elements, and n is of course len(a).