A158242 Smallest n-digit number with distinct digits such that every k-digit substring (k <= n) taken from the left is divisible by k (k = 1..n).

1, 10, 102, 1024, 10245, 102456, 1024569, 12965408, 381654720, 3816547290

Offset: 1

Author

Lekraj Beedassy, Mar 14 2009

Keywords

• nonn
• base
• fini
• full

Comments

Years ago, the columnist Alex Bellos asked John Conway for some math puzzles for his column. A few days after Conway's death in 2020, Bellos published two of those puzzles. a(10) of this sequence is the solution to the second puzzle. See the Bellos (2020) link. - Alonso del Arte, Apr 21 2020

Examples

			12965408, for instance, is in the sequence because 1|1, 2|12, 3|129, 4|1296, 5|12965, 6|129654, 7|1296540, 8|12965408. It's a(8).
		

Links

• Alex Bellos, Did you solve it? John Horton Conway, playful maths genius, The Guardian, April 20, 2020.

Crossrefs

Cf. A158240.

Extensions

a(8), a(9) corrected by Ray Chandler, Mar 21 2009