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:

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.

Solutions were received from Joseph DeVincentis, David Madfes, Philippe Fondanaiche, Denis Borris, Kirk Bresniker, and Adrian Atanasiu.  The (nearly) complete lists I received (pasted from several sources) are below.  25 is the maximum number of digits, and the answer is the same for max and min.  Notice how little the first digits change as the number of digits increases.
n  min                      max
1  1                        9
2  10                       98
3  102                      987
4  1020                     9876
5  10200                    98765
6  102000                   987654
7  1020005                  9876545
8  10200056                 98765456
9  102000564                987654564
10 1020005640               9876545640
11 10200056405              98765456405
12 102006162060             987606963096
13 1020061620604            9876069630960
14 10200616206046           98760696309604
15 102006162060465          987606963096045
16 1020061620604650         9848048850242400
17                          98440864203682569
18                          984408642036825696
19 1080548010360000180      9812523240364656789
20 10805480103600001800     96685896604836004260
21 123606009012225672009    966858966048360042609
22 1236060090122256720090   9668589660483600426096
23 12360600901222567200901  72645656402410567240820
24 144408645048225636603816 402852168072900828009216
25 3608528850368400786036725
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