A160585 Decimal expansion of (520659 +314170*sqrt(2))/521^2.

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

Offset: 1

Author

Klaus Brockhaus, Jun 08 2009

Keywords

• cons
• nonn

Comments

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A129725.

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

Examples

			(520659 +314170*sqrt(2))/521^2 = 3.55496212764746398474...
		

Links

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

Crossrefs

Cf. A129725, A160583, A002193 (decimal expansion of sqrt(2)), A160584 (decimal expansion of (537+92*sqrt(2))/521).

Programs

Magma

(520659 +314170*Sqrt(2))/521^2; // G. C. Greubel, Apr 07 2018

Maple

with(MmaTranslator[Mma]): Digits:=150:
RealDigits(evalf((520659+314170*sqrt(2))/521^2))[1]; # Muniru A Asiru, Apr 08 2018

Mathematica

RealDigits[(520659+314170Sqrt[2])/521^2,10,120][[1]] (* Harvey P. Dale, Aug 23 2011 *)

PARI

(520659 +314170*sqrt(2))/521^2 \\ G. C. Greubel, Apr 07 2018

Formula

Equals (890 +353*sqrt(2))/(890 -353*sqrt(2)).

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