A113786 Decimal expansion of the solution to the equation sqrt(n)+sqrt(n+1)+sqrt(n+2)=sqrt(9n+8).

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..100.

Formula

n=(1/24)*(2*(3*(90 + sqrt(1509)))^(1/3)+ 2*(3*(90 - sqrt(1509)))^(1/3)-9)

Example

n=0.67819352379110344286342528025892014001502874941365

Mathematica

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 *)

Crossrefs

Cf. A114458 floor(sqrt(n)+sqrt(n+1)+sqrt(n+2)).

Sequence in context: A301863 A284362 A229177 * A004487 A274137 A010500

Adjacent sequences: A113783 A113784 A113785 * A113787 A113788 A113789

Keyword

cons,nonn

Author

Zak Seidov, Jan 20 2006

Status

approved