A160576 Decimal expansion of (119187+47998*sqrt(2))/313^2.

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

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 (932 +206*sqrt(2))/(932 -206*sqrt(2)).

Equals (3+2*sqrt(2))*(26-5*sqrt(2))^2/(26+5*sqrt(2))^2.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A129640.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 1, b = A160574.

Minimal polynomial: 97969*x^2 - 238374*x + 97969. - Amiram Eldar, Apr 28 2026

Example

1.90944505472939211538735166618641701329182813618943...

Mathematica

RealDigits[(119187 +47998*Sqrt[2])/313^2, 10, 100][[1]] (* G. C. Greubel, Apr 08 2018 *)

Prog

(PARI) (119187 +47998*sqrt(2))/313^2 \\ G. C. Greubel, Apr 08 2018
(Magma) (119187 +47998*Sqrt(2))/313^2; // G. C. Greubel, Apr 08 2018

Crossrefs

Cf. A129640, A160574, A002193 (decimal expansion of sqrt(2)), A160575 (decimal expansion of (363+130*sqrt(2))/313).

Sequence in context: A198220 A131566 A264156 * A104756 A154994 A237193

Adjacent sequences: A160573 A160574 A160575 * A160577 A160578 A160579

Keyword

cons,nonn

Author

Klaus Brockhaus, Jun 08 2009

Status

approved