Describe and add

[Eric Angelini]

Could please someone compute and analyse this sequence?

Start with a(1) = 1
Describe a(1) --> = 11 (one "1")
Add a(1) to it's description: 1 + 11 = 12
This is a(2) -- so we have:
a(1) = 1
a(2) = 12

Go on from there :
Description of a(2) : 1112
Add a(2) to it's description: 12 + 1112 = 1124
This is a(3) -- we have now:
a(1) = 1
a(2) = 12
a(3) = 1124

Go on from there :
Description of a(3) : 211214
Add a(3) to it's description: 1124 + 211214 = 212338
This is a(4) -- we have now:
a(1) = 1
a(2) = 12
a(3) = 1124
a(4) = 212338

Go on from there :
Description of a(4) : 11222318
Add a(4) to it's description: 212338 + 11222318 = 11434656
This is a(5) -- we have now:
a(1) = 1
a(2) = 12
a(3) = 1124
a(4) = 212338
a(5) = 11434656

etc.

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Questions:

- has this seq. a fixed point (or loop)?
- what about other beginnings?
(start with a(1) = 0 for instance)

Best,
É.