A160205 Decimal expansion of (989043+524338*sqrt(2))/809^2.

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

Offset

11,1

Links

G. C. Greubel, Table of n, a(n) for n = 11..10000

Index entries for algebraic numbers, degree 2.

Formula

Equals (1282 +409*sqrt(2))/(1282 -409*sqrt(2)).

Equals (3+2*sqrt(2))*(29-4*sqrt(2))^2/(29+4*sqrt(2))^2.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A123654.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 1, b = A160203.

Minimal polynomial: 654481*x^2 - 1978086*x + 654481. - Amiram Eldar, May 12 2026

Example

2.64418510371971670942102194299706893113942897011738...

Mathematica

RealDigits[(989043+524338*Sqrt[2])/809^2, 10, 100][[1]] (* G. C. Greubel, Apr 25 2018 *)

Prog

(PARI) (989043+524338*sqrt(2))/809^2 \\ G. C. Greubel, Apr 25 2018
(Magma) (989043+524338*Sqrt(2))/809^2; // G. C. Greubel, Apr 25 2018

Crossrefs

Cf. A123654, A160203, A002193 (decimal expansion of sqrt(2)), A160204 (decimal expansion of (873+232*sqrt(2))/809).

Sequence in context: A216153 A100115 A029670 * A187817 A276678 A276680

Adjacent sequences: A160202 A160203 A160204 * A160206 A160207 A160208

Keyword

cons,nonn

Author

Klaus Brockhaus, May 18 2009

Status

approved