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A119906 Largest number whose factorial is less than 10^(10^n). 2
3, 13, 69, 449, 3248, 25205, 205022, 1723507, 14842906, 130202808, 1158787577, 10433891463, 94851898540, 869200494599, 8019346203785, 74419210652835, 694100859679691, 6502464891216879, 61154108320430275, 577134533044522749 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..19.

EXAMPLE

a(1) = 13 because 10^(10^1) = 10^10 = 10000000000 and 13! = 6227020800 is largest factorial less than this.

MAPLE

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, Aug 04 2006

CROSSREFS

Cf. A000142, A061010, A152909.

Sequence in context: A184818 A007808 A104989 * A059726 A274379 A192209

Adjacent sequences:  A119903 A119904 A119905 * A119907 A119908 A119909

KEYWORD

nonn

AUTHOR

Julien Peter Benney (jpbenney(AT)ftml.net), Aug 01 2006

EXTENSIONS

a(6) from R. J. Mathar, Aug 04 2006

More terms from Jon E. Schoenfield, Aug 09 2006

STATUS

approved

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Last modified June 28 15:19 EDT 2017. Contains 288838 sequences.