# [seqfan] Re: The contamination sequence

Éric Angelini eric.angelini at skynet.be
Sun Mar 29 13:36:52 CEST 2020

Case closed, sorry -- Rémy has checked
and corrected the seq in the meantime.

à+
É.
Catapulté de mon aPhone

> Le 25 mars 2020 à 18:05, Éric Angelini <bk263401 at skynet.be> a écrit :
>
> 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.
>
> -----------------------------------------
>
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