(1) n-pandigital, i.e. formed from a permutation of the digits 1 to n, with no repeat digits; and

(2) k-divisible, i.e. for all k, k ≤ n, the integer formed from the truncated left most k digits is evenly divisible by k.

And for n=10, also find all 10-digit pandigitals with the same second condition.

Example: 2136547 almost qualifies, but fails for k=2.

2136547 is divisible by 7

213654 is divisible by 6

21365 is divisible by 5

2136 is divisible by 4

213 is divisible by 3

21 is not divisible by 2

2 is divisible by 1