# Sum three terms & digits

Max Alekseyev maxale at gmail.com
Wed May 23 14:44:13 CEST 2007

```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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