Start as you wish had you prove that for any kdigit number M there exists a number n such that the string of first k digits of 2
^{n} equals M.
Find a power of 2 whose decimal expansion begins with the 12digit string "201320132013". It need not be the smallest such number.
Bonus:
Find the smallest such number and prove it to be the smallest.
(In reply to
re(2): 'Slide Rule' Logic by broll)
Yes, logarithms are needed for the terribly huge numbers involved, as well as extended precision arithmetic.
But it could be handled manually in a few steps given an available log function in extended precision calculator software.
Edited on January 2, 2013, 12:10 pm

Posted by Charlie
on 20130102 12:09:36 