Triple FJS

[Eric Angelini]

Hello SeqFans,
I'm working on "Fractal Jump Sequences" for the moment
(search the OEIS with the string "FJS"). I have found this:

(a)   1  1 3   1 1 3   1 3   1 1 3   1 1 3   1 3   1 1 1 3   3 ...
(b)  1 13 1 131 3 1 131 1 313 1 1 133 1 3 111 1 313 3 1 1 133 1 ...
     ----------------------------------------------------------
(c)  1113113131131131311133131111313311133111113313131111313331 ...
     ^
- the succession of digits in (a) and (b) are the same;
- when I "push" (a) into (b) I get (c);
- ... and (c) has the same succession of digits as (a) and (b)
      [except for the initial "1"].

Does this ring a bell to someone ? Is it of interest ?

This sequence (c) is not in the OEIS.

It is unique for the digits "1" and "3" [and FJS, of course,
                                         by construction].

... One can build as many such sequences as desired. Here is 
for "1" and "4":

(a)   1  1 4    1 1 4    1 4    1 4    1 1 1 4    4    1 1 1 4 ...
(b)  1 14 1 1414 1 4 1114 4 1114 1 4411 1 4 1 1444 1111 1 4 1 1 ...
     ----------------------------------------------------------
(c)  1114114141411144111414411141144411111411414444111111141141 ...
     ^

Those sequences seem to lack any regularity... (Do they?) Once the
construction law has been defined they self-generate automatically.

Best,
E.