A389133 Decimal expansion of the octahedral root of 2.

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

Offset

1,2

Comments

The real solution to x*(2*x^2 + 1)/3 = 2. Minimal polynomial 2*x^3+x-6.

Links

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

Index entries for algebraic numbers, degree 3.

Formula

Equals ((sqrt(2922)+54)^(2/3) - 6^(1/3)) / (6^(2/3)* (sqrt(2922)+54)^(1/3))

Example

1.326956285678968286031128931...

Mathematica

N[((Sqrt[2922] + 54)^(2/3) - 6^(1/3))/(6^(2/3) (Sqrt[2922] + 54)^(1/3)), 105]

Prog

(PARI) ((sqrt(2922)+54)^(2/3)-6^(1/3))/(6^(2/3)*(sqrt(2922)+54)^(1/3))

Crossrefs

Cf. A005900, 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), this sequence (octahedral root), A389134 (icosahedral root), A389135 (dodecahedral root).

Sequence in context: A389192 A210738 A210601 * A197493 A300070 A171632

Adjacent sequences: A389130 A389131 A389132 * A389134 A389135 A389136

Keyword

nonn,cons

Author

Kelvin Voskuijl, Sep 24 2025

Status

approved