David's recent message

[Richard Guy]

Isn't the word `ternary' ?   R.

On Fri, 17 Feb 2006, Don Reble wrote:

>> the largest numbers a(n) with no substring divisible by n, gcd(n, 10) = 1.
>>
>> n: a(n)
>>
>> 3: 88
>> 7: 999993
>> 9: 88888888
>  ...
>> 63: 99999899999899999899999899999899999899999899999899966241755974
>
>
>> - Are the above values of a(n) correct?
>
>    Yes, even the ones that I elided.
>
>    ---
>
>    But enough of this base-ten tripe: it's more interesting in base
>    three. Sometimes, there's an (n-1)-trit number with the property,
>    and sometimes there isn't.
>
> 2 1
> 4 212
> 5 2111
> 10 222111222
> 20 1121212211122121211
> 37 221122212222221122212222221122212221
>
>    Which suggests
>
> %I Axxxxxx
> %S Axxxxxx 2,4,5,10,20,37
> %N Axxxxxx Numbers n, coprime to 3, such that there exists an (n-1)-digit trinary number, wherein each substring is indivisible by n.
> %C Axxxxxx a(5) > 64
> %e Axxxxxx 20 is there, because each substring of 1121212211122121211 (base 3) is indivisible by 20.
> %K Axxxxxx nonn,base,new
> %O Axxxxxx 1,1
> %E Axxxxxx Don Reble (djr(AT)nk.ca), Feb 17 2006
>
>    Cruel exercise for seqfans: (since one may insert "1") prove whether
>    the sequence equals A018620.
>
> -- 
> Don Reble  djr at nk.ca
>
> -- 
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