A383955 Decimal expansion of sqrt(5/3 - 2*sqrt(1/45)).

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

Offset

1,3

Comments

Let v_10 be a degree-10 vertex and v_3 be a degree-3 vertex of a triakis icosahedron centered at the origin. Then this is the ratio of norm(v_10)/norm(v_3).

The minimal polynomial is 45*x^4 - 150*x^2 + 121.

One choice of coordinates for the triakis icosahedron describes a degree-10 vertex of the triakis icosahedron as (0,1,(1+sqrt(5))/2) and a degree-3 vertex as ((5+7*sqrt(5))/22)*(1, 1, 1).

Links

Table of n, a(n) for n=1..87.

Wikipedia, Triakis icosahedron, As a Catalan solid.

Index entries for algebraic numbers, degree 2.

Example

1.169839420461925922675809622142811611361278...

Mathematica

RealDigits[Sqrt[(25 - 2*Sqrt[5])/15], 10, 100][[1]]

Prog

(PARI) sqrt(5/3-2*sqrt(1/45)) \\ Charles R Greathouse IV, May 19 2026

Crossrefs

Cf. A378973, A378974, A378975, A378976, A378977, A380793, A380794, A382009.

Sequence in context: A266563 A397290 A382197 * A335028 A153603 A198557

Adjacent sequences: A383952 A383953 A383954 * A383956 A383957 A383958

Keyword

nonn,cons

Author

Peter Kagey, Aug 19 2025

Status

approved