The Radix Economy of a number in a particular base is the number of digits needed to express it in that base, multiplied by the base. In functional form we write: , where E is the radix econony, b and N, are the base and number, respectively, and , is the number of digits of the base-b representation of N.
For example, if and , then the radix economy is :
>> E = 2 * length(dec2bin(1000))
>> E =
20
Given a base b, and an integer n, calculate , for .
For example, if and , we have:
>> F = 3 * length(dec2base(factorial(10),3))
>> F =
42
----------------
NOTE: As it is, this problem is quite simple. In fact, a solution is already given for small values of b and n. Therefore, to make it a bit interesting, some built-in functions are disabled.
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