The string of the base ten numbers 4k-3, 4k-2, 4k-1 and 4k written side by side without commas or spaces is denoted by F(k). For example:

F(1) = 1234, F(2) = 5678, F(3) = 9101112, F(4) = 13141516 - and, so on.

Determine the remainder when this expression is divided by 7. What is the remainder when this expression is divided by 13?

F(1) + F(2) + F(3) + ..... + F(2011)