A159892 Decimal expansion of (450483+287918*sqrt(2))/439^2.

4, 4, 5, 0, 2, 7, 0, 2, 8, 9, 4, 4, 0, 8, 8, 4, 9, 0, 7, 5, 1, 3, 3, 7, 2, 2, 5, 3, 6, 5, 6, 8, 8, 1, 4, 5, 7, 5, 7, 6, 6, 1, 4, 8, 3, 1, 8, 8, 0, 1, 7, 9, 8, 2, 1, 2, 5, 9, 1, 4, 2, 8, 8, 9, 4, 7, 6, 5, 7, 8, 6, 4, 8, 5, 8, 4, 4, 9, 7, 4, 5, 7, 0, 0, 6, 3, 7, 6, 4, 6, 1, 8, 7, 2, 5, 8, 2, 1, 5, 9, 3, 8, 4, 3, 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 (802 + 359*sqrt(2))/(802 - 359*sqrt(2)).

Equals (3 + 2*sqrt(2))*(21 - sqrt(2))^2/(21 + sqrt(2))^2.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 0, b = A130645.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = 1, b = A159890.

Minimal polynomial: 192721*x^2 - 900966*x + 192721. - Amiram Eldar, May 10 2026

Example

4.45027028944088490751337225365688145757661483188017...

Mathematica

RealDigits[N[(450483+287918*Sqrt[2])/439^2, 300]][[1]] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011 *)

Prog

(PARI) (450483+287918*sqrt(2))/439^2 \\ G. C. Greubel, May 17 2018
(Magma) (450483 +287918*Sqrt(2))/439^2; // G. C. Greubel, May 17 2018

Crossrefs

Cf. A130645, A159890, A002193 (decimal expansion of sqrt(2)), A159891 (decimal expansion of (443+42*sqrt(2))/439).

Sequence in context: A239351 A111481 A111763 * A255241 A200694 A021696

Adjacent sequences: A159889 A159890 A159891 * A159893 A159894 A159895

Keyword

cons,nonn

Author

Klaus Brockhaus, Apr 30 2009

Status

approved