[seqfan] English seq spelling itself

[Eric Angelini]

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.