A360830 Numbers that when concatenated with the natural numbers from 1 to N are divisible by the corresponding order number.

1, 3, 6, 42, 84, 252, 2772, 36036, 612612, 11639628, 267711444, 803134332, 23290895628, 722017764468, 1444035528936, 53429314570632, 2190601897395912, 94195881588024216, 4427206434637138152, 30990445042459967064

Offset: 1

Author

Rodolfo Kurchan, Feb 22 2023

Keywords

• nonn
• base

Comments

There is an elevator with the numbers from 1 to N. Each number goes up in the elevator and can go up as long as the concatenation of this number with the number of the floor (1 to N) is a multiple of the floor.

Example, the number 1 reaches floor 2, because 11 is divisible by 1, 12 is divisible by 2, but it does not reach floor 3 because 13 is not divisible by 3.

The sequence shows the numbers that can go higher in the elevator than the previous number.

For example, 2 cannot go higher than 1, so it does not appear, instead number 3 can go up to floor 3, since 31 is divisible by 1, 32 is divisible by 2 and 33 is divisible by 3, instead I couldn't get to floor 4 because 34 is not divisible by 4.

Examples

			42 goes after 6, because it is the smallest number that can go more than the 6th floor that can go number 6. 421, 422, 423, 424, 425, 426 and 427 are divisible by 1, 2, 3, 4, 5, 6 and 7, but 42 cannot go to floor 8th, because 428 it is not divisible by 8.
   n |         a(n)         | Maximum Elevator floor
  ---------------------------------------------------
   1 |                    1 |          2
   2 |                    3 |          3
   3 |                    6 |          6
   4 |                   42 |          7
   5 |                   84 |          8
   6 |                  252 |         10
   7 |                 2772 |         12
   8 |                36036 |         16
   9 |               612612 |         18
  10 |             11639628 |         22
  11 |            267711444 |         26
  12 |            803134332 |         28
  13 |          23290895628 |         30
  14 |         722017764468 |         31
  15 |        1444035528936 |         36
  16 |       53429314570632 |         40
  17 |     2190601897395912 |         42
  18 |    94195881588024216 |         46
  19 |  4427206434637138152 |         48
  20 | 30990445042459967064 |         52
  ...
		

References

• Jaime Poniachik, Problem El Ascensor, La Odisea del Ingenio, May 1990.

Crossrefs

Cf. A285201, A286282.