A160582 Decimal expansion of (213651 +31850*sqrt(2))/457^2.

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

Offset

1,2

Comments

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A129642.

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A160580.

A quadratic number with minimal polynomial 208849*x^2 - 427302*x + 208849. - Charles R Greathouse IV, Dec 06 2016

Links

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

Index entries for algebraic numbers, degree 2

Formula

Equals (650 +49*sqrt(2))/(650 -49*sqrt(2)).

Equals (3 +2*sqrt(2))*(23 -6*sqrt(2))^2/(23 +6*sqrt(2))^2.

Example

(213651 +31850*sqrt(2))/457^2 = 1.23866382870678373994...

Maple

with(MmaTranslator[Mma]): Digits:=150:
RealDigits(evalf((213651+31850*sqrt(2))/457^2))[1]; # Muniru A Asiru, Apr 08 2018

Mathematica

RealDigits[(213651+31850Sqrt[2])/457^2, 10, 120][[1]] (* Harvey P. Dale, Jan 06 2013 *)

Prog

(PARI) (213651+31850*sqrt(2))/457^2 \\ Charles R Greathouse IV, Dec 06 2016
(Magma) (213651 +31850*Sqrt(2))/457^2; // G. C. Greubel, Apr 07 2018

Crossrefs

Cf. A129642, A160580, A002193 (decimal expansion of sqrt(2)), A160581 (decimal expansion of (601+276*sqrt(2))/457).

Sequence in context: A321336 A093098 A021423 * A321668 A112977 A120390

Adjacent sequences: A160579 A160580 A160581 * A160583 A160584 A160585

Keyword

cons,nonn

Author

Klaus Brockhaus, Jun 08 2009

Status

approved