[seqfan] Re: Aitken-like array -- with digits

Eric Angelini Eric.Angelini at kntv.be
Tue Oct 6 15:24:03 CEST 2009


Waow -- many thanks, Hans! If M. Aitken is "Alexander Aitken"
(http://en.wikipedia.org/wiki/Alexander_Aitken), your result
would have challenged him!

> Aitken was one of the best mental calculators known, and had
  a prodigious memory (...)

Best,
É.


-----Message d'origine-----
De : seqfan-bounces at list.seqfan.eu 
[mailto:seqfan-bounces at list.seqfan.eu] 
De la part de Hans Havermann
Envoyé : mardi 6 octobre 2009 14:40
À : Sequence Fanatics Discussion list
Objet : [seqfan] Re: Aitken-like array -- with digits

On 29 September 2009, Eric Angelini wrote:

> 1.
> 1,2.
> 2,3,5.
> 5,7,1 0,6.
> 6,1 1,8,2,8,8.
> 8,1 4,2,5,1 0,7,9,8.
> 8,1 6,2,1 0,4,6,1,4,1 3,1 0,1 2.
> 2,1 0,2,6,4,7,4,1 1,1 0,2,5,2,3,3,5,3,5.
> 5,7,8,8,1 0,7,4,1 4,8,2,5,9,2,7,1 4,4,1 0,4,9,7,6.
> 6,1 1,8,9,1 6,1 0,1,1 3,5,1,5,9,5,1 0,1 0,7,1 6,6,5,4,2,0,1 1,1 0,1  
> 3,1 2.
> 2,8,9,1 0,9,9,1 0,1 5,2,0,2,6,5,5,3,1 1,1 4,1 0,4,1,2,1,1 1,2,6,1  
> 0,6,6,3,1,2,3,7,1,1,9,7,5.
> 5,7,1 5,1 0,6,1,9,1 5,2,9,2,1 0,4,9,4,7,5,9,1 2,5,8,6,1  
> 3,2,2,9,9,8,2,4,3,4,1 5,1 0,8,8,1 0,6,5,3,8,8,1,9,1 7,8,5.
> 5,1 0,8,1,1 3,2,1,9,3,1 0,1 0,8,3,9,3,1,8,7,1 8,7,8,1 3,1 6,2,1 0,1  
> 2,1 6,7,4,4,8,4,1 0,9,9,4,5,9,1 1,5,9,9,4,9,8,1 0,...
>
> Left border: 1,1,2,5,6,8,8,2,5,6,2,5,5,...

> ObPuzzle:
>
> See what is written between two commas as an integer; those integers  
> are in the range 0 <--> 18 (0+0 <--> 9+9).
> Replace, in said array, 1 with A, 2 with B, 3 with C... 16 with P,  
> 17 with Q, 18 with R... and 0 with T (!)
>
> At which row will one read A,I,T,K,E,N at some point?


You had to pick a particularly difficult letter-combination. The first  
time that I-T (90) even shows up is in row #56 (...7909...). The good  
news is that the digits 11514, a minimum requirement for K-E-N, occurs  
542 times in that row. Row #56 has over four-million digits in it and  
the length of each subsequent row appears to be about 1.286 times the  
length of its predecessor, so it is unlikely that anyone will venture  
into that realm.


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