A396213 Decimal expansion of sqrt(9 + 6*sqrt(3)).

4, 4, 0, 3, 6, 6, 9, 4, 7, 5, 0, 4, 1, 6, 1, 1, 6, 7, 6, 1, 5, 3, 6, 6, 3, 4, 7, 6, 0, 0, 8, 5, 9, 8, 1, 2, 8, 9, 5, 9, 2, 3, 7, 1, 0, 7, 8, 0, 8, 8, 6, 0, 1, 0, 6, 6, 1, 5, 3, 1, 1, 3, 0, 9, 5, 4, 4, 8, 8, 8, 4, 1, 0, 6, 8, 1, 3, 8, 6, 3, 1, 8, 9, 3, 2, 5, 0, 9, 0, 7, 4, 2, 5, 4, 7, 7, 2, 8, 2, 2, 7, 2, 3, 2, 7

Offset

1,1

Comments

The largest value of the constant k such that a^3 + b^3 + c^3 >= 3*a*b*c + k*(a-b)*(b-c)*(c-a) for all nonnegative a, b, c.

Links

Table of n, a(n) for n=1..105.

M. S. Klamkin and D. J. Newman, Problem 71-28, An Inequality, SIAM Review, Vol. 13, No. 4 (1971), p. 572; Solution, by C. C. Rousseau, ibid., Vol. 14, No. 4 (1972), pp. 656-657.

Index entries for algebraic numbers, degree 4.

Formula

Minimal polynomial: x^4 - 18*x^2 - 27.

Equals sqrt(A385259 - 1).

Example

4.40366947504161167615366347600859812895923710780886...

Mathematica

RealDigits[Sqrt[9 + 6*Sqrt[3]], 10, 120][[1]]

Prog

(PARI) sqrt(9 + 6*sqrt(3))

Crossrefs

Cf. A385259.

Sequence in context: A187149 A106508 A392472 * A177036 A158100 A104287

Adjacent sequences: A396210 A396211 A396212 * A396214 A396215 A396216

Keyword

nonn,cons

Author

Amiram Eldar, May 19 2026

Status

approved