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

Hans Havermann pxp at rogers.com
Tue Oct 6 14:40:02 CEST 2009

```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.

```