There exists an integer 
such that every string in the look
and say sequence "decays" in at most 
days to a compound of "common" and "transuranic
elements."
The table below gives the periodic table of atoms associated with the look and say sequence as named by Conway (1987). The "abundance" is the
average number of occurrences for long strings out of every million atoms. The asymptotic
abundances are zero for transuranic elements, and 27.246... for arsenic (As), the
next rarest element. The most common element is hydrogen (H), having an abundance
of 
.
The starting element is U, represented by the string "3," and subsequent
terms are those giving a description of the current term: one three (13); one one,
one three (1113); three ones, one three (3113), etc.
See also
Conway's Constant, Look and Say Sequence
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References
Conway, J. H. "The Weird and Wonderful Chemistry of Audioactive Decay." §5.11 in Open Problems in Communication and Computation (Ed. T. M. Cover and B. Gopinath). New York: Springer-Verlag, pp. 173-188, 1987.Conway, J. H. "The Weird and Wonderful Chemistry of Audioactive Decay." Eureka, 5-18, 1985.Ekhad, S. B. and Zeilberger, D. "Proof of Conway's Lost Cosmological Theorem." Electronic Research Announcement of the Amer. Math. Soc. 3, 78-82, 1997. http://www.math.temple.edu/~zeilberg/mamarim/mamarimhtml/horton.html.Hilgemeier, M. "Die Gleichniszahlen-Reihe." Bild der Wissensch. 12, 194-196, Dec. 1986.Hilgemeier, M. "'One Metaphor Fits All': A Fractal Voyage with 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.Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 905, 2002.
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Cite this as:
Weisstein, Eric W. "Cosmological Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CosmologicalTheorem.html