David's recent message

[Don Reble]

> 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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