A119906 Largest number whose factorial is less than 10^(10^n).

3, 13, 69, 449, 3248, 25205, 205022, 1723507, 14842906, 130202808, 1158787577, 10433891463, 94851898540, 869200494599, 8019346203785, 74419210652835, 694100859679691, 6502464891216879, 61154108320430275, 577134533044522749, 5463531774867094396

Offset: 0

Author

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

Keywords

• nonn

Examples

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

Links

• Daniel Suteu, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000142, A061010, A152909.

Programs

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 *)

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