A176522 Decimal expansion of (9+sqrt(85))/2.

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

Offset

1,1

Comments

Continued fraction expansion of (9+sqrt(85))/2 is A010734.

Links

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

Wikipedia, Metallic mean.

Index entries for algebraic numbers, degree 2.

Formula

Equals lim_{n->oo} S(n, sqrt(5*17))/S(n-1, sqrt(5*17)), with the S-Chebyshev polynomials (see A049310). - Wolfdieter Lang, Nov 15 2023

Minimal polynomial: x^2 - 9*x - 1. - Amiram Eldar, May 04 2026

Example

9.10977222864644365500113714088139657862340252436123...

Mathematica

First[RealDigits[(9 + Sqrt[85])/2, 10, 100]] (* Paolo Xausa, Jun 18 2024 *)

Prog

(PARI) (9+sqrt(85))/2 \\ Charles R Greathouse IV, Jul 24 2013

Crossrefs

Cf. A010536 (decimal expansion of sqrt(85)), A010734 (all 9's sequence), A333345, A049310.

Sequence in context: A324998 A020841 A081801 * A219732 A259314 A266557

Adjacent sequences: A176519 A176520 A176521 * A176523 A176524 A176525

Keyword

nonn,cons,easy

Author

Klaus Brockhaus, Apr 23 2010

Status

approved