A003019 Number of distinct values taken by 4^4^...^4 (with n 4's and parentheses inserted in all possible ways).

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• more

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.
• Index entries for sequences related to parenthesizing
• MathOverflow discussion of related questions

Crossrefs

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

Extensions

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

a(24)-a(25) from Marek Hubal, Mar 01 2019