A389135 Decimal expansion of the dodecahedral root of 2.

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

Offset

1,3

Comments

The real solution to x*(3*x - 1)*(3*x - 2)/2 = 2. Minimum polynomial 9*x^3-9*x^2+2*x-4.

Links

Kelvin Voskuijl, Table of n, a(n) for n = 1..20000

Index entries for algebraic numbers, degree 3.

Formula

Equals (3^(4 / 3) * (sqrt(2913) + 54)^(1 / 3) + (4374 - 81 * sqrt(2913))^(1 / 3) + 9) / 27.

Example

1.144947122738966941651535584...

Mathematica

N[(1/27) (9 + (4374 - 81 Sqrt[2913])^(1/3) + 3 (3 (54 + Sqrt[2913]))^(1/3)), 105]

Prog

(PARI) (3^(4/3)*(sqrt(2913)+54)^(1/3)+(4374-81*sqrt(2913))^(1/3)+9)/27

Crossrefs

Cf. A006566, A002193 (square root of 2), A222133 (triangular root of 2), A188934 (hexagonal root of 2).

Platonic figurate roots of 2: A002580 (cube root), A388148 (tetrahedral root), A389133 (octahedral root), A389134 (icosahedral root), this sequence (dodecahedral root).

Sequence in context: A019627 A137617 A345732 * A023405 A160900 A035116

Adjacent sequences: A389132 A389133 A389134 * A389136 A389137 A389138

Keyword

cons,nonn,changed

Author

Kelvin Voskuijl, Sep 24 2025

Status

approved