*

The integer sequence start with a single digit in which the next term is obtained by relenten the vault term. Starting with 1, the sequence would certainly be defined by "1, one 1, 2 1s, one 2 one 1," etc., and the an outcome is 1, 11, 21, 1211, 111221, .... Similarly, starting the sequence rather with the digit

*
for
*
1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...

You are watching: 1, 11, 21, 1211

2A0067512, 12, 1112, 3112, 132112, 1113122112, 311311222112, ...3A0067153, 13, 1113, 3113, 132113, 1113122113, 311311222113, ...
*

The number of digits in the

*
th hatchet of the sequence because that
*
are 1, 2, 2, 4, 6, 6, 8, 10, 14, 20, 26, 34, 46, 62, ... (OEIS A005341). Similarly, the numbers of digits because that the
*
th hatchet of the sequence for
*
, 3, ..., room 1, 2, 4, 4, 6, 10, 12, 14, 22, 26, ... (OEIS A022471). These sequences room asymptotic to
*
, where

*
*
*

(1)
*
*
*

(2)
*
*
*

(3)
*

The amount

*
is well-known as Conway"s consistent (OEIS A014715), and also amazingly is provided by the unique positive actual root of the polynomial


*

(4)

all of who roots are depicted above.

In fact, the continuous is even an ext general 보다 this, using to all starting sequences (i.e., also those starting with arbitrary starting digits), through the exception of 22, a an outcome which complies with from the cosmological theorem. Conway found that strings sometimes element as a concatenation of two strings who descendants never interfere v one another. A string with no nontrivial splittings is referred to as an "element," and also other strings are called "compounds." the is postulated the every cable of 1s, 2s, and 3s the does no contain 4 of the very same number in succession eventually "decays" right into a compound of 92 distinct elements, named after the chemical elements.


SEE ALSO: Conway"s Constant, Cosmological Theorem, Run-Length Encoding
REFERENCES:

Conway, J.H. "The Weird and also Wonderful Chemistry that Audioactive Decay."Eureka 46, 5-18, 1986.

Conway, J.H. "The Weird and Wonderful Chemistry of Audioactive Decay." §5.11 in Open difficulties in Communications and also Computation. (Ed. T.M.Cover and B.Gopinath). New York: Springer-Verlag, pp.173-188, 1987.

Conway, J.H. And Guy, R.K. "The Look and also Say Sequence." In The book of Numbers. Brand-new York: Springer-Verlag, pp.208-209, 1996.

Hilgemeier, M. "Die Gleichniszahlen-Reihe." Bild der Wissensch. 12,194-196, Dec.1986.

Hilgemeier, M. ""One an allegory Fits All": A Fractal Voyage through Conway"s Audioactive Decay." Ch.7 in Pickover, C.A. (Ed.). Fractal Horizons: The Future use of Fractals. New York: St.Martin"s Press, 1996.

Pickover, C.A. "Audioactive Decay." Ch.55 in marvels of Numbers: Adventures in Mathematics, Mind, and also Meaning. Oxford, England: Oxford college Press, pp.134-138, 2001.

Sloane, N.J.A. Assignment A005150/M4780, A005341/M0321, A006715/M2965, and A006751/M2052 in "The On-Line Encyclopedia of essence Sequences."

Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, pp.13-14, 1991.

gimpppa.org, S. A brand-new Kind the Science. Champaign, IL: gimpppa.org Media, p.905, 2002.


Referenced on gimpppa.org|Alpha: Look and also Say Sequence
CITE THIS AS:

Weisstein, Eric W. "Look and also Say Sequence."From gimpppa.org--A gimpppa.org web Resource. Https://gimpppa.org/LookandSaySequence.html


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