单词 | Look and Say Sequence | ||||||||||||||||||
释义 | Look and Say SequenceThe Integer Sequence beginning with a single digit in which the next term is obtained by describing the previous term.Starting with 1, the sequence would be defined by ``one 1, two 1s, one 2 two 1s,'' etc., and the result is 1, 11, 21,1211, 111221, 312211, 13112221, 1113213211, ... (Sloane's A005150). Starting the sequence instead with the digit ![]() (Sloane's A014715) is Conway's Constant. ![]()
In fact, the constant is even more general than this, applying to all starting sequences (i.e., even thosestarting with arbitrary starting digits), with the exception of 22, a result which follows from the CosmologicalTheorem. Conway discovered that strings sometimes factor as a concatenation of two strings whose descendants neverinterfere with one another. A string with no nontrivial splittings is called an ``element,'' and other strings arecalled ``compounds.'' Every string of 1s, 2s, and 3s eventually ``decays'' into a compound of 92 special elements,named after the chemical elements. See also Conway's Constant, Cosmological Theorem
Conway, J. H. ``The Weird and Wonderful Chemistry of Audioactive Decay.'' Eureka 45, 5-18, 1985. Conway, J. H. ``The Weird and Wonderful Chemistry of Audioactive Decay.'' §5.11 in Open Problems in Communications and 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 Say Sequence.'' In The Book of Numbers. New York: Springer-Verlag, pp. 208-209, 1996. Sloane, N. J. A. SequencesA005150/M4780,A006715/M2965, andA006751/M2052in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995. Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, pp. 13-14, 1991. |
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