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

Author

Paolo Xausa, Nov 09 2024

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			0.94315125924388181712671989257036415940665038623453...
		

Links

• Wikipedia, Snub dodecahedron.
• Index entries for algebraic numbers, degree 6.

Crossrefs

Cf. A001622, A377805, A377806, A377807.

Programs

Mathematica

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

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

Formula

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