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A003019 Number of distinct values taken by 4^4^...^4 (with n 4's and parentheses inserted in all possible ways).
(Formerly M1179)
17
1, 1, 2, 4, 9, 20, 48, 114, 282, 703, 1787, 4583, 11900, 31131, 82117, 217954, 581970, 1561704, 4210263, 11396488, 30963024, 84402984, 230779071, 632762424, 1739387089 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
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]
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
CROSSREFS
Sequence in context: A186952 A034823 A036625 * A036626 A036722 A318800
KEYWORD
nonn,nice,more
AUTHOR
EXTENSIONS
a(12)-a(23) from Jon E. Schoenfield, Oct 11 2008
a(24)-a(25) from Marek Hubal, Mar 01 2019
STATUS
approved

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Last modified May 18 09:54 EDT 2024. Contains 372620 sequences. (Running on oeis4.)