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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, 5463531774867094396 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Daniel Suteu, Table of n, a(n) for n = 0..500 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 MATHEMATICA With[{s = Array[Factorial, 30000]}, Table[LengthWhile[s, # < 10^(10^n) &], {n, 0, 5}] ] (* Michael De Vlieger, May 14 2018 *) 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 a(7)-a(19) from Jon E. Schoenfield, Aug 09 2006 a(20) from Daniel Suteu, May 14 2018 STATUS approved

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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)