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A061010
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Number of digits in (10^n)!.
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4
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1, 7, 158, 2568, 35660, 456574, 5565709, 65657060, 756570557, 8565705523, 95657055187, 1056570551816, 11565705518104, 125657055180975, 1356570551809683, 14565705518096757, 155657055180967491
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Jerry Glynn and Theodore Gray, "The Beginner's Guide To Mathematica, Version 4," Cambridge University Press, Cambridge, UK, 2000, p. 26.
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LINKS
| Barbarel Tres Mil, Table of n, a(n) for n = 0..200
Enrique Perez Herrero, TRAILING ZEROS IN n! , Psychedelic Geometry Blogspot
Eric Weisstein's World of Mathematics, Factorial
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FORMULA
| 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+delta(n,0)+floor((-2*10^n+log(2)+(1+2*10^n)*n*log(10)+log(pi))/(2*log(10))) (End)
a(n) = 10^n*(n - 1/log(10)) + n/2 + O(1). [Arkadiusz Wesolowski, Jan 21 2012]
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MATHEMATICA
| Table[ Floor[ N[ Log[ 10, (10^n)! ]] + 1 ], {n, 0, 7} ]
$MaxPrecision = Infinity; A061010[n_] := 1 + KroneckerDelta[n, 0] + Floor[(-2*10^n + Log[2] + (1 + 2*10^n)*n*Log[10] + Log[Pi])/(2*Log[10])] (* Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Nov 09 2009 *)
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CROSSREFS
| Cf. A000142, A034886.
Sequence in context: A009703 A014385 A114485 * A153714 A153713 A137995
Adjacent sequences: A061007 A061008 A061009 * A061011 A061012 A061013
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KEYWORD
| nonn,base
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), May 20 2001
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EXTENSIONS
| a(7) from Farideh Firoozbakht (mymontain(AT)yahoo.com), Jul 05 2005
More terms from Eric Weisstein (eric(AT)weisstein.com), Dec 01 2005
Typo in formula fixed, and Mathematica formula changed to cover a(0)=1 Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Feb 06 2010
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