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%I #20 Feb 17 2020 12:07:12
%S 3,4,8,9,2,5,1,3,1,1,6,4,3,0,6,6,5,7,6,7,1,2,7,8,4,8,9,8,0,7,7,0,6,5,
%T 1,5,4,9,1,6,3,7,1,1,3,2,6,5,0,9,8,1,7,3,3,9,6,6,2,5,0,1,5,6,5,4,2,8,
%U 1,8,0,9,7,6,3,6,3,9,4,2,1,7,6,0,7,2,0,6,0,8,9,5,4,0,2,9,0,8,3,2,8,3,6,8,5,5,0,1,7,7,0,3,7,8,9,2,6,0,8,4,9,3,7
%N Decimal expansion of root of (x+1)^sqrt(x) = sqrt(x)^(x+1).
%e 3.4892513116430665767127848980770651549163711326509817339662501...
%p Digits:=200:fsolve((x+1)^sqrt(x)-sqrt(x)^(x+1) =0, x,0..10);
%t RealDigits[x/.FindRoot[(x+1)^Sqrt[x]==(Sqrt[x])^(x+1),{x,3}, WorkingPrecision -> 150]][[1]] (* _Harvey P. Dale_, Feb 17 2020 *)
%o (PARI) solve(x=3,4,(x+1)^sqrt(x)-sqrt(x)^(x+1)) \\ _Charles R Greathouse IV_, Aug 26 2017
%K nonn,cons
%O 1,1
%A _Michel Lagneau_
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