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A117607
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Integer complexity of n represented with {1,+,!} and parentheses, where ! can be concatenated for multifactorials.
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0
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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; internal format)
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OFFSET
| 1,2
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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. See also: n! = A000142. n!! = A006882. n!!! = A007661. n!!!! = A007662. n!!!!! = A085157. n!!!!!! = A085158. n!!!!!!! = A114799. n!!!!!!!! = A114800. n!!!!!!!!! = A114806.
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LINKS
| Ed Pegg, Jr., Integer Complexity
Eric Weisstein's World of Mathematics, Multifactorial.
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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.
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CROSSREFS
| Cf. A000142, A006882, A007661, A007662, A085157, A085158, A114799, A114800, A114806.
Sequence in context: A134364 A104413 A127064 * A194551 A088492 A025492
Adjacent sequences: A117604 A117605 A117606 * A117608 A117609 A117610
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 06 2006
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