OFFSET
1,2
COMMENTS
The sequence starts with a(1) = 1 and is always extended with the smallest integer not yet present in the sequence that does not lead to a contradiction.
Leading zeros must be erased from the divisor: the pair [10,11] is thus accepted because 1011 is divisible by 1.
Lars Blomberg (in a private mail):
...The integer 21 is never used because:
...Let the previous number be x*10 + y, the new number is 21.
...Then x*1000 + y*100 + 21 (which is odd) must be divisible by y*10+2
...which is even, not possible.
...The same goes for 23, 25, 27, 29 and 41, 43, 45, 47, 49 and many more.
LINKS
Lars Blomberg, Table of n, a(n) for n = 1..10000
EXAMPLE
The concatenation [12] is divisible by 12, of course. A similar situation applies for the pairs [23], [34], [45], etc. When it comes to [910] we see that 910 is divisible by 91 (concatenation of 9 and 1, which are the last and first digits of the pair [9,10]). As we consider that [1011] is divisible by 1 (see the comment section), we accept that the integer 11 comes immediately after 10. But 12 cannot follow now, as [1112] is not divisible by 11. We have then to wait until 28 shows up as [1128] is divisible by 12 (quotient = 94). Etc.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Eric Angelini and Lars Blomberg, Mar 13 2018
STATUS
approved