cp's OEIS Frontend

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

%I A360830 #22 May 12 2024 10:05:29
%S A360830 1,3,6,42,84,252,2772,36036,612612,11639628,267711444,803134332,
%T A360830 23290895628,722017764468,1444035528936,53429314570632,
%U A360830 2190601897395912,94195881588024216,4427206434637138152,30990445042459967064
%N A360830 Numbers that when concatenated with the natural numbers from 1 to N are divisible by the corresponding order number.
%C A360830 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.
%C A360830 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.
%C A360830 The sequence shows the numbers that can go higher in the elevator than the previous number.
%C A360830 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.
%D A360830 Jaime Poniachik, Problem El Ascensor, La Odisea del Ingenio, May 1990.
%e A360830 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.
%e A360830    n |         a(n)         | Maximum Elevator floor
%e A360830   ---------------------------------------------------
%e A360830    1 |                    1 |          2
%e A360830    2 |                    3 |          3
%e A360830    3 |                    6 |          6
%e A360830    4 |                   42 |          7
%e A360830    5 |                   84 |          8
%e A360830    6 |                  252 |         10
%e A360830    7 |                 2772 |         12
%e A360830    8 |                36036 |         16
%e A360830    9 |               612612 |         18
%e A360830   10 |             11639628 |         22
%e A360830   11 |            267711444 |         26
%e A360830   12 |            803134332 |         28
%e A360830   13 |          23290895628 |         30
%e A360830   14 |         722017764468 |         31
%e A360830   15 |        1444035528936 |         36
%e A360830   16 |       53429314570632 |         40
%e A360830   17 |     2190601897395912 |         42
%e A360830   18 |    94195881588024216 |         46
%e A360830   19 |  4427206434637138152 |         48
%e A360830   20 | 30990445042459967064 |         52
%e A360830   ...
%Y A360830 Cf. A285201, A286282.
%K A360830 nonn,base
%O A360830 1,2
%A A360830 _Rodolfo Kurchan_, Feb 22 2023