“Hofstadter-Conway $10,000 Sequence”的概念、定义、习题解题方法及翻译-数学辞典

单词

Hofstadter-Conway $10,000 Sequence

释义

Hofstadter-Conway $10,000 Sequence

The Integer Sequence defined by the Recurrence Relation

with

. The first few values are 1, 1, 2, 2, 3, 4, 4, 4, 5, 6, ... (Sloane's A004001). Plotting

against

gives the Batrachion plotted below. Conway (1988) showed that

andoffered a prize of $10,000 to the discoverer of a value of

for which

for

. The prize wassubsequently claimed by Mallows, after adjustment to Conway's ``intended'' prize of $1,000 (Schroeder 1991), who found

takes a value of 1/2 for of the form with , 2, .... Pickover (1996) gives a table ofanalogous values of corresponding to different values of .

See also Blancmange Function, Hofstadter's Q-Sequence, Mallow's Sequence

References

Conolly, B. W. ``Meta-Fibonacci Sequences.'' In Fibonacci and Lucas Numbers, and the Golden Section (Ed. S. Vajda). New York: Halstead Press, pp. 127-138, 1989.

Conway, J. ``Some Crazy Sequences.'' Lecture at AT&T Bell Labs, July 15, 1988.

Guy, R. K. ``Three Sequences of Hofstadter.'' §E31 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 231-232, 1994.

Kubo, T. and Vakil, R. ``On Conway's Recursive Sequence.'' Disc. Math. 152, 225-252, 1996.

Mallows, C. ``Conway's Challenging Sequence.'' Amer. Math. Monthly 98, 5-20, 1991.

Pickover, C. A. ``The Drums of Ulupu.'' In Mazes for the Mind: Computers and the Unexpected. New York: St. Martin's Press, 1993.

Pickover, C. A. ``The Crying of Fractal Batrachion 1,489.'' Ch. 25 in Keys to Infinity. New York: W. H. Freeman, pp. 183-191, 1995.

Schroeder, M. ``John Horton Conway's `Death Bet.''' Fractals, Chaos, Power Laws. New York: W. H. Freeman, pp. 57-59, 1991.

Sloane, N. J. A. SequenceA004001/M0276in ``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.

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