A160042 Decimal expansion of (89+36*sqrt(2))/73.

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

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Index entries for algebraic numbers, degree 2.

Formula

Equals (9+2*sqrt(2))/(9-2*sqrt(2)).

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A129289.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A160041.

Minimal polynomial: 73*x^2 - 178*x + 73. - Amiram Eldar, May 10 2026

Example

1.91659846911549892817617526125409768258230393854205...

Mathematica

RealDigits[(89+36Sqrt[2])/73, 10, 120][[1]] (* Harvey P. Dale, Jun 19 2011 *)

Prog

(PARI) (89+36*sqrt(2))/73 \\ G. C. Greubel, Apr 15 2018
(Magma) (89+36*Sqrt(2))/73; // G. C. Greubel, Apr 15 2018

Crossrefs

Cf. A129289, A160041, A002193 (decimal expansion of sqrt(2)), A160043 (decimal expansion of (5907+1802*sqrt(2))/73^2).

Sequence in context: A176519 A010535 A154902 * A264934 A363876 A195712

Adjacent sequences: A160039 A160040 A160041 * A160043 A160044 A160045

Keyword

cons,nonn

Author

Klaus Brockhaus, May 04 2009

Status

approved