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Search: id:A119906
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| A119906 |
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Largest number whose factorial is less than 10^(10^n). |
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+0
1
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| 3, 13, 69, 449, 3248, 25205, 205022, 1723507, 14842906, 130202808, 1158787577, 10433891463, 94851898540, 869200494599, 8019346203785, 74419210652835, 694100859679691, 6502464891216879, 61154108320430275, 577134533044522749
(list; graph; listen)
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OFFSET
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0,1
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EXAMPLE
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a(1) = 13 because 10^(10^1) = 10^10 = 10000000000 and 13! = 6227020800 is largest factorial less than this.
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MAPLE
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A119906Stirling := proc(n) local i; fsolve( (i+0.5)*log(i+1.0)=log(10.0)*10.0^n+i-1.0-0.5*log(2.0*Pi)-1./12.0/i, i) ; end : A119906 := proc(n::integer) local aestim::integer, resul::integer, faci1::integer, faci::integer, pow10::integer, i ; pow10 := 10^(10^n) ; aestim := floor(A119906Stirling(n))-1 ; faci1 := factorial(aestim) ; for i from aestim+1 to aestim+9 do faci := factorial(i) ; if faci1< pow10 and faci >= pow10 then RETURN(i-1) ; fi ; faci1 := faci ; end ; RETURN(0) ; end: for n from 0 to 30 do printf("%d, ", A119906(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 04 2006
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CROSSREFS
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Cf. A000142, A061010.
Sequence in context: A088368 A007808 A104989 this_sequence A059726 A154677 A121586
Adjacent sequences: A119903 A119904 A119905 this_sequence A119907 A119908 A119909
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KEYWORD
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nonn
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AUTHOR
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Julien Peter Benney (jpbenney(AT)ftml.net), Aug 01 2006
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EXTENSIONS
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a(6) from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 04 2006
More terms from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Aug 09 2006
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