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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 A309079 A194551

Adjacent sequences:  A117604 A117605 A117606 * A117608 A117609 A117610

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Apr 06 2006

STATUS

approved

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Last modified February 21 01:03 EST 2020. Contains 332086 sequences. (Running on oeis4.)