# [seqfan] The contamination sequence

Éric Angelini bk263401 at skynet.be
Wed Mar 25 18:05:03 CET 2020

Hello SeqFans,
I think some issues here might be interesting:
(copy/paste from the draft < https://oeis.org/draft/A333501) >)

I would appreciate if someone could compute 10000 terms or so:
I would like to see the graph and be sure that the sequence
doesn't stop before the 10000th term.
Best,
É.

-------------------------------------------------------------
The contamination sequence: a digit d must be separated at least by d non-d digits from any other digit d; this is the lexicographically earliest sequence of distinct integers with this property.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 30, 21, 31, 24, 32, 50, 23, 40, 25, 34, 26, 35, 27, 38, 29, 36, 41, 37, 28, 39, 42, 51, 60, 43,...

EXAMPLE:
a(18) = 19 and a(19) = 20; what could come next?

Not a(20) = 11 (the smallest unused term in the sequence) because 11 is forever banned (at least one digit, which is not 1, must separate the two 1s);

not a(20) = 21 as there is only one digit between the 2 of 20 and the 2 of 21 (the digits' succession would be 202 and we want at least two non-2 digits, between two 2s);

not a(20) = 22 (of course), nor 23, 24, ... 29 as all those integers start with 2;

a(20) = 30 is ok.

What comes next? Not a(21) = 11, of course, but a(21) = 21 is ok, as there are more than 2 non-2 digits beween the 2 of 20 and the 2 of 21 (the digits' succession here is 20302, which is ok);

What next? Not a(22) = 11 or 22 (banned forever) and not a 2-digit integer starting with 2; thus a(22) = 31, smallest term not used before that doesn't lead to an immediate contradiction. Etc.

-----------------------------------------