
__problem_title__ = "Phigital number base"
__problem_url___ = "https://projecteuler.net/problem=473"
__problem_description__ = "Let $\varphi$ be the golden ratio: $\varphi=\frac{1+\sqrt{5}}{2}.$ " \
                          "Remarkably it is possible to write every positive integer as a sum of " \
                          "powers of $\varphi$ even if we require that every power of $\varphi$ " \
                          "is used at most once in this sum. Even then this representation is " \
                          "not unique. We can make it unique by requiring that no powers with " \
                          "consecutive exponents are used and that the representation is finite. " \
                          "E.g: $2=\varphi+\varphi^{-2}$ and $3=\varphi^{2}+\varphi^{-2}$ To " \
                          "represent this sum of powers of $\varphi$ we use a string of 0's and " \
                          "1's with a point to indicate where the negative exponents start. We " \
                          "call this the representation in the . So $1=1_{\varphi}$, " \
                          "$2=10.01_{\varphi}$, $3=100.01_{\varphi}$ and " \
                          "$14=100100.001001_{\varphi}$. The strings representing 1, 2 and 14 in " \
                          "the phigital number base are palindromic, while the string " \
                          "representating 3 is not. (the phigital point is not the middle " \
                          "character). The sum of the positive integers not exceeding 1000 whose " \
                          "phigital representation is palindromic is 4345. Find the sum of the " \
                          "positive integers not exceeding $10^{10}$ whose phigital " \
                          "representation is palindromic."

import timeit


class Solution():

    @staticmethod
    def solution1():
        pass

    @staticmethod
    def time_solutions():
        setup = 'from __main__ import Solution'
        print('Solution 1:', timeit.timeit('Solution.solution1()', setup=setup, number=1))


if __name__ == '__main__':
    s = Solution()
    print(s.solution1())
    s.time_solutions()

