Fwd: No string of digits divisible by k

[Maximilian Hasler]

---------- Forwarded message ----------
From: Maximilian Hasler <maximilian.hasler at gmail.com>
Date: Jun 12, 2007 2:20 PM
Subject: Re: No string of digits divisible by k
To: Eric Angelini <Eric.Angelini at kntv.be>


Eric,
in case you intend to submit this, consider rephrasing the definition
in a way making it a clear and precise definition:
"having a string of digits divisible by 3" is very ambiguos
1/ the only digits divisible by 3 are 0,3,6,9

2/ zero is divisible by 3 so zeroless is useless
(btw I'm not sure if this word exists)

3/ a "string" divisible by 3 ? Strings are not numbers ! A string may
be divided (split up) in substrings...

4/ I think you mean "substring"

5/ The sequence IS finite and there are no terms with more than 2
digits: the remainder of a(n) divided by 3 is 1 or 2, and the same is
true for the first and last digit ; so removing either one or both of
these digits, you get a "substring" divisible by 3.

Maximilian

On 6/12/07, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
> Hello SeqFans,
> could someone examine this sequence:
>
> - Zeroless integers having no string of digits divisible by 3.
>
> I think it starts like this:
>
> 1,2,4,5,7,8,11,14,17,22,25,28,41,44,47,52,... (not OEIS)
>
> ... but I'm quite sure the sequence is finite. Example:
>
> 715 will not fit because "15" is a substring divisible by 3;
> 716 neither because "6" is divisible by 3,
> 717 neither because "717" is divisible by 3;
> 718 neither because of "18";
> 719 neither because of "9";
> 720 neither (has a "0")
> etc.
>
> If we replace the definition by:
>
> - Zeroless integers having no string of digits divisible by k.
>
> ... what could be the smallest k leading to an infinite sequence
> -- if such k exists -- or to the longest finite sequence?
>
> Sorry if this is hold hat.
>
> Best,
> É.
>
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