Probe with exponential increase then binary search lowest unused in distributed hash table - dictionary

Question

I need advice how to aproach this task. The autor has created function find_next_free_dataset_num(node) and it searching for free slots in distributed hash table. This DHT uses dictionary like interface which override __setitem__, __getitem__ and __contains__. Which is good design. But this function uses linear probing now for searching new unused slot for predictable key. So the question is if exponential num = num*num + 1 solves it and how to implement binary search on new num value between 0 and used slot num?

def predictable_key(node, num):
    return "monitor_dataset_{0}_{1}".format(node.get_address(), str(num))


def find_next_free_dataset_num(node):
    # FIXME probe with exponential increase then binary search lowest unused
    num = 0
    while node[predictable_key(node, num)] is not None:
        _log.info("Dataset {0} already exists!".format(num))
        num += 1
    return num