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A003019
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Number of distinct values taken by 4^4^...^4 (with n 4's and parentheses inserted in all possible ways).
(Formerly M1179)
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13
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1, 1, 2, 4, 9, 20, 48, 114, 282, 703, 1787, 4583, 11900, 31131, 82117, 217954, 581970, 1561704, 4210263, 11396488, 30963024, 84402984, 230779071
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| See also the Four Fours puzzle [Bourke]. Four fours is a mathematical puzzle. The goal of four fours is to find the simplest mathematical expression for every whole number from 0 to some maximum, using only common mathematical symbols and the digit four (no other digit is allowed). The subsequence of primes begins 2, 1787, 4583, no more through a(23). [Jonathan Vos Post, Apr 02 2011]
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis, Amer. Math. Monthly 80 (8) (1973), 868-876.
Paul Bourke, Four Fours Problem.
Index entries for sequences related to parenthesizing
MathOverflow discussion of related questions
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CROSSREFS
| Cf. A002845, A003018, A145545, A145546, A145547, A145548, A145549, A145550, A000081.
Sequence in context: A186952 A034823 A036625 * A036626 A036722 A034824
Adjacent sequences: A003016 A003017 A003018 * A003020 A003021 A003022
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KEYWORD
| nonn,nice,more
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| a(12) - a(23) from Jon Schoenfield (jonscho(AT)hiwaay.net), Oct 11 2008
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