A159692 Decimal expansion of (2052963 + 1343918*sqrt(2))/881^2.

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

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 (1682 + 799*sqrt(2))/(1682 - 799*sqrt(2)).

Equals (3 + 2*sqrt(2))*(42 - sqrt(2))^2/(42 + sqrt(2))^2.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A130014.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 1, b = A159690.

Minimal polynomial: 776161*x^2 - 4105926*x + 776161. - Amiram Eldar, May 09 2026

Example

5.09372419165266633056217448037513998043601300170046...

Mathematica

RealDigits[(2052963 + 1343918*Sqrt[2])/881^2, 10, 100][[1]] (* G. C. Greubel, Jun 02 2018 *)

Prog

(PARI) (2052963 + 1343918*sqrt(2))/881^2 \\ G. C. Greubel, Jun 02 2018
(Magma) (2052963 + 1343918*Sqrt(2))/881^2; // G. C. Greubel, Jun 02 2018

Crossrefs

Cf. A130014, A159690, A002193 (decimal expansion of sqrt(2)), A159691 (decimal expansion of (883+42*sqrt(2))/881).

Sequence in context: A266439 A132706 A199184 * A271175 A367740 A196769

Adjacent sequences: A159689 A159690 A159691 * A159693 A159694 A159695

Keyword

cons,nonn

Author

Klaus Brockhaus, Apr 21 2009

Status

approved