

A117607


Integer complexity of n represented with {1,+,!} and parentheses, where ! can be concatenated for multifactorials.


1



1, 2, 3, 4, 5, 3, 4, 4, 5, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 6, 4, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 3, 4, 5, 5
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Using the set of symbols {1, +, !} and parentheses, how many 1's does it take to represent n? "!!" is double factorial, "!!!" is triple factorial and so forth.
lim inf = 3, lim sup = infinity. What is the average behavior of this sequence?  Charles R Greathouse IV, Jun 15 2012


LINKS

Table of n, a(n) for n=1..39.
Ed Pegg, Jr., Integer Complexity
Eric Weisstein's World of Mathematics, Multifactorial.
Index to sequences related to the complexity of n


EXAMPLE

a(1) = 1 because there is one 1 in "1".
a(2) = 2 because "1 + 1".
a(6) = 3 because "(1+1+1)!".
a(7) = 4 because "(1+1+1)!+1".
a(8) = 4 because "(1+1+1+1)!!" using double factorial.
a(12) = 3 because "((1+1+1)!)!!!!" using quadruple factorial.
a(15) = 5 because "(1+1+1+1+1)!!" using double factorial.
a(16) = 4 because "((1+1+1+1)!!)!!!!!!" using double factorial and sextuple factorial.
a(24) = 3 because "(((1+1+1)!)!!!!)!!!!!!!!!!" using quadruple factorial and decuple factorial.
a(36) = 3 because "(((1+1+1)!)!!!!)!!!!!!!!!" using quadruple factorial and nonuple factorial.


CROSSREFS

n! = A000142. n!! = A006882. n!!! = A007661. n!!!! = A007662. n!!!!! = A085157. n!!!!!! = A085158. n!!!!!!! = A114799. n!!!!!!!! = A114800. n!!!!!!!!! = A114806.
Sequence in context: A104413 A127064 A279850 * A215092 A345018 A309079
Adjacent sequences: A117604 A117605 A117606 * A117608 A117609 A117610


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Apr 06 2006


STATUS

approved



