The integer sequence start with a single digit in which the following term is acquired by describing the vault term. Starting with 1, the sequence would be identified by "1, one 1, two 1s, one 2 one 1," etc., and the an outcome is 1, 11, 21, 1211, 111221, .... Similarly, starting the sequence rather with the digit

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

You are watching: 1, 11, 21, 1211, 111221, 312211

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

The number of digits in the

th term 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, ..., space 1, 2, 4, 4, 6, 10, 12, 14, 22, 26, ... (OEIS A022471). These sequences room asymptotic come
, where





The amount

is recognized as Conway"s constant (OEIS A014715), and amazingly is provided by the distinctive positive actual root that the polynomial



all of whose roots are portrayed above.

In fact, the consistent is even an ext general than this, applying to all beginning sequences (i.e., also those beginning with arbitrary starting digits), through the exception of 22, a an outcome which complies with from the cosmological theorem. Conway discovered that strings sometimes variable as a concatenation of two strings whose descendants never interfere through one another. A string through no nontrivial splittings is referred to as an "element," and also other strings are dubbed "compounds." the is postulated that every wire of 1s, 2s, and also 3s that does not contain 4 of the same number in sequence eventually "decays" into a link of 92 distinct elements, called after the chemical elements.

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

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

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

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

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

Hilgemeier, M. ""One metaphor Fits All": A Fractal Voyage v 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 university 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 creature Sequences."

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

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

Referenced ~ above keolistravelservices.com|Alpha: Look and Say Sequence

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

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