# Sum three terms & digits

Eric Angelini Eric.Angelini at kntv.be
Wed May 23 14:50:22 CEST 2007

```Hello Alex,

Yes, you are right:

- seq S is monotonically increasing
- S starts with 1,2,3 (or 0,1,2)
- the next term you want to add to S must be the smallest
one not infringing the rule

I think this defines better S.

Best,
É.

-----Message d'origine-----
De : Max Alekseyev
[mailto:maxale at gmail.com]
Envoyé : mercredi 23 mai 2007 14:44
À : Eric Angelini
Cc : seqfan at ext.jussieu.fr
Objet : Re: Sum three terms & digits

Eric,

It is not clear how the sequence is defined.
Say, why it starts as 1,2,3,... and not as 1,2,1,... or as 1,2,2,... ?
Can you give a precise definition of this sequence?

Max

On 5/23/07, Eric Angelini <Eric.Angelini at kntv.be> wrote:
>
>
> Hello Seq-Fans,
>
> Is this sequence finite? I guess yes:
>
> S = 1,2,3,4,5,7,8,9,10,14,15,31,32,33,34,35,37,38,39,40,42...
>
> Sum three consecutive terms of S: the result cannot share
> any single digit with any of the three considered terms.
>
> Examples:
>
> 1+2+3=6 and "6" has no common digit with 1 or 2 or 3
> 8+9+10=27 and "27" has no common digit with 8 or 9 or 10
>
> But:
>
> 9+10+11=30 and "30" shares the digit "0" with "10" -- thus
>            "11" is not written after 10
> 9+10+12=31 and "31" shares the digit "1" with "10" (and "12")
>            thus "12" is not written after 10
> 9+10+13=32 and "32" shares "3"... thus... no "13"
>
> Now:
>
> 9+10+14=33 and "33" shares nothing, thus 33 is written after
>            9,10, etc.
>
> Best,
> É.
>
>
>

```

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