[seqfan] Re: English seq spelling itself

[M. F. Hasler]

Hello Eric,

It took me some time to understand that & why you use a 10 to group the
digits which correspond to the number which codes a letter.
I wondered why you don't leave the digits together, and what this would
give.
It seems that 20 is the only number equal to the "code" of its first letter,
so this variant must start :
20 => twenty => (20, 23, 5, 14, 20, 25) => twenty, twenty-three, five, ....
=> (20, 23, 5, 14, 20, 25 ; 20, 23, 5, 14, 20, 25, 20, 8, 18, 5, 5 ; 6, 9,
22, 5 ; ...)

Then I found that another variant of this already exists : A104059
<https://oeis.org/A104059>
where a 0 is inserted to delimit terms, to avoid the apparent ambiguity of,
e.g., the second term being "twenty-three" or "twenty" followed by "three"
as the next term.
But actually there is no ambiguity because we know that the second term is
the code of the second letter of the first term.
Alternatively, one could also preserve the (not so)"special" character(s)
"comma" as well as (optionally) "hyphen" and "space".
So we have several variants of A104059:
(the above) A = twenty, twentythree, five, fourteen, ...
= 20, 23, 5, 14, 20, 25 ; 20, 23, 5, 14, 20, 25, 20, 8, 18, 5, 5 ; 6, 9,
22, 5 ; ...

B = twenty comma twentythree comma five comma fourteen comma ..
= 20,23,5,14,20,25,  3,15,13,13,1,  20,23,5,14,20,25,20,8,18,5,5,
 3,15,13,13,1, ...

C = twenty comma twenty hyphen three comma ..
= 20,23,5,14,20,25,  3,15,13,13,1,  20,23,5,14,20,25,  8,25,16,8,5,14,
 20,8,18,5,5,

(and maybe other variants),
but spelling out the comma and hyphen also suggests the idea of spelling
out the individual digits, so we get back to something closer to your
second example:
D = two zero comma two three comma one five comma ...
= 20,23,15,  26,5,18,15,  3,15,13,13,1,   20,23,15,  20,8,18,5,5,
3,15,13,13,1, ...

In some sense this is a "dual" version of yours:
Your sequence are the digits (+separator 10) which glued together yield the
code of the letters of the sequence spelled out in English;
the above D lists the codes of the letters of the sequence spelled out
digit/character-wise in English.

Here, 2 is the only digit this sequence can start with, because no other
digit is equal to the first digit of the code of the first letter of its
name in English.

Maximilian

On Fri, Feb 5, 2016 at 1:50 PM, Eric Angelini <Eric.Angelini at kntv.be> wrote:

>
> Hello SeqFans,
> A string hereunder like "ONE FIVE TEN" is coding a single letter.
> (Here the letter "O"). All successive strings end with TEN. The only
> thing you have to do to decipher the message is to replace the words
> before TEN by the digits they suggest: "ONE FIVE TEN" becomes 1 5.
> You see where I want to go: "15" is the rank of "O" in the alphabet...
>
> ONE FIVE TEN ONE FOUR TEN FIVE TEN SIX TEN NINE TEN TWO TWO TEN FIVE TEN
> TWO ZERO TEN FIVE TEN ONE FOUR TEN ...
> ------------              --------         --------             --------
>             --------
>      15          14           5       6        9        22          5
>    20          5         14
>
>       O           N           E       F        I         V          E
>     T          E          N
>
> This means that the sequence S, with the above set of rules, is coding
> itself: S = 1,5,10,1,4,10,5,10,6,10,9,10,2,2,10,5,10,2,0,10,5,10,1,4,10,...
>
> There are only two such “self-coding” seq in English; here is the 2d one:
>
> T = 2,0,10,2,3,10,1,5,10,2,6,10,5,10,1,8,10,1,5,10,2,0,10,5,10,1,4,10,...
>
> Let’s check:
>
> 2,0,10,2,3,10,1,5,10,2,6,10,5,10,1,8,10,1,5,10,2,0,10,5,10,1,4,10,...
>  20     23     15     26    5     18     15     20    5     14
>   T      W      O      Z    E      R      O      T    E      N
>
> ... which spells T again.
>
> Best,
> É.
>
>