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%I #26 Jan 22 2016 16:29:12
%S 3,4,5,9,8,6,5,6,4,4,0,4,4,9,9,9,1,3,4,1,8,7,8,6,1,0,8,1,0,6,8,9,8,1,
%T 2,0,2,7,7,5,1,8,4,5,9,9,0,6,4,2,8,3,1,4,5,2,9,8,0,6,8,8,7,2,8,5,8,2,
%U 5,2,2,1,2,1,1,1,4,5,1,3,1,3,8,9,7,9,2
%N Decimal expansion of the real number x between 3 and 4 where 2^x = x!.
%C 2^3 > 3! but 2^4 < 4!. Since the exponential and generalized factorial (Gamma) functions are continuous, it follows that 2^x = x! ( = gamma(x+1) ) for some x between 3 and 4. It's about 3.45986564404500.
%H WolframAlpha, <a href="http://www.wolframalpha.com/input/?i=solve+gamma%28n%2B1%29%3D2^n">Find value</a>
%t RealDigits[x/.FindRoot[2^x==x!,{x,3,4},WorkingPrecision->120]][[1]] (* _Harvey P. Dale_, Jan 22 2016 *)
%o (PARI) solve(x=3, 4, 2^x-gamma(x+1)) \\ _Michel Marcus_, Aug 03 2013
%K nonn,cons
%O 1,1
%A _Colm Mulcahy_, Dec 19 2011
%E More terms from _D. S. McNeil_, Dec 19 2011
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