[ n + reverse(n) ] consists entirely of odd (decimal) digits.

For instance, 36 + 63 = 99 and 409 + 904 = 1313.

We will call such numbers reversible; so 36, 63, 409, and 904 are reversible. Leading zeroes are not allowed in either n or reverse(n).

There are 120 reversible numbers below one-thousand.

a. Evaluate how many reversible numbers are there

below **10 ^{k}, k=2,3... up to 6 or 7 **.

b. Analyze the results, aiming to find the relation (i.e. approximate function) between **N(k) and k**.

Source: Project Euler, modified.