> 1
> 11
> 12
> 2111
> 1321
> 11213111
> 1331112112
> 211221133211

> where each line is formed by "look and say" from the
> previous, and then reversed.  (Seehttp://en.wikipedia.org/wiki/Look-and-say_sequence
> for the standard look-and-say sequence.)

> This sequence is A022481 in Sloane.  (Equivalently,
> and perhaps more naturally, the sequence of the
> reverses of the above is A006711).

> The lengths of these strings is A022476 in Sloane:

> 1, 2, 2, 4, 4, 8, 10, 12, 14, 20, 24, 30, 38, 54, 66, 92,
> 120, 160, 210, 284, 378, 490, 632, 852, 1134, ....

> Whereas the asymptotic growth rate of the standard
> look-and-say sequence is

> 1.303577269034296391257...

> (an algebraic integer of degree 71), numerical
> experimentation indicates the asymptotic growth
> rate of the reverse sequence is approximately

> 1.327.

> As in the standard case, this growth rate is
> independent of the initial condition.

> Is anyone aware of an analysis of this reverse
> case?  E.g., what are the "elements" and what
> is the minimal polynomial for the asymptotic
> growth rate?

> I computed 56 terms before running out of
> memory in Mathematica, which was not
> enough to find a linear recurrence (which
> would yield the minimal polynomial).

> 1
> 11
> 12
> 2111
> 1321
> 11213111
> 1331112112
> 211221133211

> where each line is formed by "look and say" from the
> previous, and then reversed.  (Seehttp://en.wikipedia.org/wiki/Look-and-say_sequence
> for the standard look-and-say sequence.)

> This sequence is A022481 in Sloane.  (Equivalently,
> and perhaps more naturally, the sequence of the
> reverses of the above is A006711).