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Search: id:A061010
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| A061010 |
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Number of digits in (10^n)!. |
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+0
3
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| 1, 7, 158, 2568, 35660, 456574, 5565709, 65657060, 756570557, 8565705523, 95657055187, 1056570551816, 11565705518104, 125657055180975, 1356570551809683, 14565705518096757, 155657055180967491
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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Jerry Glynn and Theodore Gray, "The Beginner's Guide To Mathematica, Version 4," Cambridge University Press, Cambridge, UK, 2000, page 26.
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LINKS
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Eric Weisstein's World of Mathematics, Factorial
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FORMULA
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Contribution from Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Nov 09 2009: (Start)
a(n)=1+floor(log((10^n)!)/(log(10)), and using Stirling aproximation:
a(n)=1+floor((-2*10^n+log(2)+(1+2*10^n)*n*log(10)+log(pi))/(2*log(10)) (End)
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MATHEMATICA
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Table[ Floor[ N[ Log[ 10, (10^n)! ]] + 1 ], {n, 0, 7} ]
A061010[ n_ ]:=1+Floor[ (-2^(1+n) 5^n+Log[ 2 ]+(1+2^(1+n) 5^n) n Log[ 10 ]+Log[ \[ Pi ] ])/Log[ 100 ] ] [ From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Nov 09 2009 ]
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CROSSREFS
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Sequence in context: A009703 A014385 A114485 this_sequence A153714 A153713 A137995
Adjacent sequences: A061007 A061008 A061009 this_sequence A061011 A061012 A061013
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KEYWORD
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nonn,base,new
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), May 20 2001
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EXTENSIONS
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One more term from Farideh Firoozbakht (mymontain(AT)yahoo.com), Jul 05 2005
Extended by Eric Weisstein (eric(AT)weisstein.com), Dec 1, 2005
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