This site is supported by donations to The OEIS Foundation.



Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A002845 Number of distinct values taken by 2^2^...^2 (with n 2's and parentheses inserted in all possible ways).
(Formerly M1139 N0435)
1, 1, 1, 2, 4, 8, 17, 36, 78, 171, 379, 851, 1928, 4396, 10087, 23273, 53948, 125608, 293543, 688366, 1619087, 3818818, 9029719, 21400706, 50828664, 120963298, 288405081 (list; graph; refs; listen; history; text; internal format)



a(n) <= A002955(n) [From Max Alekseyev, Sep 23 2009]


F. Goebel and R. P. Nederpelt, The number of numerical outcomes of iterated powers, Amer. Math. Monthly, 80 (1971), 1097-1103.

R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis. Amer. Math. Monthly 80 (1973), 868-876.

J. Q. Longyear, personal communication.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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..27.

Jon E. Schoenfield, The 851 values for n=12

R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis (annotated cached copy)

Index entries for sequences related to parenthesizing

MathOverflow discussion of related questions


When n=3, 2^(2^2) = (2^2)^2 = 16, so a(3) = 1.


Cf. A003018, A003019, A145545, A145546, A145547, A145548, A145549, A145550, A000081.

Sequence in context: A190162 A157904 A182901 * A072925 A002955 A202844

Adjacent sequences:  A002842 A002843 A002844 * A002846 A002847 A002848




N. J. A. Sloane.


a(12)-a(13) corrected and a(14)-a(27) added by Jon E. Schoenfield, Oct 11 2008



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 22 18:48 EST 2014. Contains 252365 sequences.