A117607 Integer complexity of n represented with {1,+,!} and parentheses, where ! can be concatenated for multifactorials.

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

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