[seqfan] Aitken-like array -- with digits

Eric Angelini Eric.Angelini at kntv.be
Tue Sep 29 18:13:16 CEST 2009



Hello SeqFans,
here is a stupid Aitken-like array:
http://www.research.att.com/~njas/sequences/A011971 
... dealing with digits only;

- start the first row with 1
- a new row starts with the last digit of the previous one
- the successive digits on the same row are given by 'vertical sum'
- 'vertical sum': add to digit 'd' the digit exactly above 'd' and
  write the result at the right of 'd'
- if the vertical sum exceeds 9, separate the digits with a space
- proceed till the end of the row.

We see here that the 4th row shows the 'vertical sum' 7+3 at the
right of 7 like this: < 7,1  0, > which is the correct way to do

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,...

Voilà... Should the left border enter the OEIS? If yes, could
someone please compute a few more terms?

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?
;-)
Best,
É.




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