A377849 Decimal expansion of the real root of x^3 + 2*x^2 - phi^2, where phi is the golden ratio (A001622).

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

Offset

0,1

Comments

Ratio of the midradius of a snub dodecahedron to the midradius of the icosahedron in which it is inscribed (see Wikipedia article).

Links

Table of n, a(n) for n=0..89.

Wikipedia, Snub dodecahedron.

Index entries for algebraic numbers, degree 6.

Formula

Equals the real root closest to 1 of x^6 + 4*x^5 + 4*x^4 - 3*x^3 - 6*x^2 + 1.

Example

0.94315125924388181712671989257036415940665038623453...

Mathematica

First[RealDigits[Root[#^3 + 2*#^2 - GoldenRatio^2 &, 1], 10, 100]]

Prog

(PARI) polrootsreal(x^6 + 4*x^5 + 4*x^4 - 3*x^3 - 6*x^2 + 1)[4] \\ Charles R Greathouse IV, Feb 10 2025

Crossrefs

Cf. A001622, A377805, A377806, A377807.

Sequence in context: A179587 A223709 A050016 * A033329 A097326 A282100

Adjacent sequences: A377846 A377847 A377848 * A377851 A377852 A377853

Keyword

nonn,cons,easy,changed

Author

Paolo Xausa, Nov 09 2024

Status

approved