euler_686.py


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#!/usr/bin/pypy

import math

# calculate the length-l prefix of 2^n
def prefix_power2(n,l):
    log = math.log10(2)*n
    declog = log - math.floor(log)
    return math.floor(pow(10,declog+l-1))

def main():
    i = 0
    count = 0
    while count < 678910:
        i = i + 1
        if prefix_power2(i, 3) == 123:
            count = count + 1
            if count % 1000 == 0:
                print("p({},{})={}".format(123,count,i))

    print("p({},{})={}".format(123,count,i))

if __name__ == "__main__":
    main()