Searching An Infinite Array
December 9, 2016
Given an array of positive integers in ascending order, of infinite size, find the index of an integer k in the array, or determine that it does not exist. Your solution must work in time logarithmic in the index of the requested integer.
Your task is to write a program that finds the requested integer. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.
Programming Praxis 
A solution in Python
def search(iterable, x): section = [next(iterable)] n = 1 while section[-1] < x: n *= 2 section = list(islice(iterable, n)) ind = bisect.bisect_left(section, x) return ind + n - 1 if section[ind] == x else Nonejust do binary search for the first n elements which will be in logarthimic time