%I #4 Apr 25 2018 17:38:46
%S 6,7,8,1,9,3,5,2,3,7,9,1,1,0,3,4,4,2,8,6,3,4,2,5,2,8,0,2,5,8,9,2,0,1,
%T 4,0,0,1,5,0,2,8,7,4,9,4,1,3,6,5,4,1,1,3,2,2,2,1,7,2,5,7,0,5,4,9,5,0,
%U 1,5,8,1,7,5,1,7,3,5,6,4,2,6,3,4,2,9,3,7,0,5,5,1,2,4,3,2,9,9,6,2
%N Decimal expansion of the solution to the equation sqrt(n)+sqrt(n+1)+sqrt(n+2)=sqrt(9n+8).
%F n=(1/24)*(2*(3*(90 + sqrt(1509)))^(1/3)+ 2*(3*(90 - sqrt(1509)))^(1/3)-9)
%e n=0.67819352379110344286342528025892014001502874941365
%t RealDigits[n/.FindRoot[Sqrt[n ]+Sqrt[n+1]+Sqrt[n+2]==Sqrt[9n+8],{n,1},WorkingPrecision->120]][[1]] (* _Harvey P. Dale_, Apr 25 2018 *)
%Y Cf. A114458 floor(sqrt(n)+sqrt(n+1)+sqrt(n+2)).
%K cons,nonn
%O 1,1
%A _Zak Seidov_, Jan 20 2006