A160584 Decimal expansion of (537+92*sqrt(2))/521.

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

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 (23+2*sqrt(2))/(23-2*sqrt(2)).

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A129725.

Equals lim_{n -> oo} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A160583.

Minimal polynomial: 521*x^2 - 1074*x + 521. - Amiram Eldar, Apr 28 2026

Example

1.28043694383555613145826365187580081233859848855024...

Maple

with(MmaTranslator[Mma]): Digits:=150:
RealDigits(evalf((537+92*sqrt(2))/521))[1]; # Muniru A Asiru, Apr 08 2018

Mathematica

RealDigits[(537 +92*Sqrt[2])/521, 10, 100][[1]] (* G. C. Greubel, Apr 07 2018 *)

Prog

(PARI) (537 +92*sqrt(2))/521 \\ G. C. Greubel, Apr 07 2018
(Magma) (537 +92*Sqrt(2))/521; // G. C. Greubel, Apr 07 2018

Crossrefs

Cf. A129725, A160583, A002193 (decimal expansion of sqrt(2)), A160585 (decimal expansion of (520659+314170*sqrt(2))/521^2).

Sequence in context: A136664 A086728 A118292 * A191334 A251794 A321595

Adjacent sequences: A160581 A160582 A160583 * A160585 A160586 A160587

Keyword

cons,nonn

Author

Klaus Brockhaus, Jun 08 2009

Status

approved