def ulam_sequence(u = 1, v = 2, n = 10):
    print()
    try:
        # Input manipulation just for fun :)
        if u == v or any(map(lambda x: int(x) != x or x < 1, (u, v))) or int(n) != n:
            raise ValueError
    except ValueError:
        print('ValueError: All arguments should be integer, and the first two should be different and positive.')
        print((u, v, n), end = ' => ')
        n = int(abs(n))
        if n > 0:
            u, v = map(lambda x:x if x > 0 else x + 1, map(lambda x:int(abs(x)), (u, v)))
            v = v if u != v else u + 1
    finally:
        print((u, v, n), end = ': ')
        if n == 0:
            print([])
            return []
        seq = sorted([u, v])
        seq2 = seq
        while len(seq) < n:
            # Test the first half of the sequence. To be proven?
            new = seq[-1] + 1
            while len(list(filter(lambda i : new - seq[i] in seq and new != seq[i]
                + seq[i], range(len(seq) // 2 + (1 if len(seq) > 4 else 0))))) != 1:
                new += 1
            seq.append(new)
        while len(seq2) < n:
            # Test the full sequence
            new = seq2[-1] + 1
            while len(list(filter(lambda i : new - seq2[i] in seq2 and new != seq2[i]
                + seq2[i], range(len(seq2))))) != 2:
                new += 1
            seq2.append(new)
        print(seq[:n] if seq == seq2 else (seq[:n], seq2[:n]))
        return seq[:n] if seq == seq2 else seq2[:n]

ulam_sequence()
ulam_sequence(4, 7, 0)
ulam_sequence(-1.3, .5)