Start as you wish
had you prove that for any k-digit number M there exists a number n such that the string of first k digits of 2n
Find a power of 2 whose decimal expansion begins with the 12-digit string "201320132013". It need not be the smallest such number.
Find the smallest such number and prove it to be the smallest.
(In reply to 'Slide Rule' Logic
Of course 2^1363 (integer power) begins "20131868734285".
It's unfortunate the original formulation mentioned a number n, but the idea is for an integer, otherwise we could use just 2^log2(201320132013) where log2(201320132013) ~= 37.5507004927368408372497476346649
Posted by Charlie
on 2013-01-01 03:30:07