Problem 217

Balanced Numbers

A positive integer with `k` (decimal) digits is called balanced if its first ^{k}/_{2} digits sum to the same value as its last ^{k}/_{2} digits, where `x`, pronounced ceiling of `x`, is the smallest integer `x`, thus π = 4 and 5 = 5.

So, for example, all palindromes are balanced, as is 13722.

Let T(`n`) be the sum of all balanced numbers less than 10^{n}.

Thus: T(1) = 45, T(2) = 540 and T(5) = 334795890.

Find T(47) mod 3^{15}

**
These problems are part of
Project Euler
and are licensed under
CC BY-NC-SA 2.0 UK
**