A157123 Decimal expansion of (11 + 3*sqrt(2))/(11 - 3*sqrt(2)).

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

Offset

1,1

Links

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

Index entries for algebraic numbers, degree 2.

Formula

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A157119.

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A157120.

Minimal polynomial: 103*x^2 - 278*x + 103. - Amiram Eldar, May 05 2026

Example

2.25570966132644925457195588153242789500580916286289...

Mathematica

RealDigits[(11 + 3*Sqrt[2])/(11 - 3*Sqrt[2]), 10, 100][[1]] (* G. C. Greubel, Jan 27 2018 *)

Prog

(PARI) (11+3*sqrt(2))/(11-3*sqrt(2)) \\ G. C. Greubel, Jan 27 2018
(Magma) (11+3*Sqrt(2))/(11-3*Sqrt(2)); // G. C. Greubel, Jan 27 2018

Crossrefs

Cf. A157119, A157120, A157121 (decimal expansion of 11+3*sqrt(2)), A157122 (decimal expansion of 11-3*sqrt(2)).

Sequence in context: A053246 A219651 A168391 * A265764 A308768 A213032

Adjacent sequences: A157120 A157121 A157122 * A157124 A157125 A157126

Keyword

cons,nonn

Author

Klaus Brockhaus, Feb 25 2009

Status

approved