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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)
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; text; internal format)



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]


N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..23.

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


Cf. A002845, A003018, A145545, A145546, A145547, A145548, A145549, A145550, A000081.

Sequence in context: A186952 A034823 A036625 * A036626 A036722 A318800

Adjacent sequences:  A003016 A003017 A003018 * A003020 A003021 A003022




N. J. A. Sloane.


a(12) - a(23) from Jon E. Schoenfield, Oct 11 2008



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Last modified January 18 11:33 EST 2019. Contains 319271 sequences. (Running on oeis4.)