Successive Digit Division

1. Find the largest integer N, such that the number made of the first k digits is divisible by k, for k=1,2,3,...,n, with n equal to the number of digits in N.  (Solve for n from 1 to 15.)
2. Repeat, finding the smallest positive integer N in each case.

Some sites with divisibility tests:

• http://mathworld.wolfram.com/DivisibilityTests.html
• http://www.7and13divisibility.com/

Source: Philippe Fondanaiche.  Similar to a previous puzzle.  It was pointed out to me that this was the same puzzle as used on IBM's Ponder This.