A160208 Decimal expansion of (1208787 +678878*sqrt(2))/857^2.

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

Offset: 1

Author

Klaus Brockhaus, May 18 2009

Keywords

• cons
• nonn

Comments

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A129857.

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A160206.

Examples

			(1208787 +678878*sqrt(2))/857^2 = 2.95305116461009821041...
		

Links

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

Crossrefs

Cf. A129857, A160206, A002193 (decimal expansion of sqrt(2)), A160207 (decimal expansion of (907+210*sqrt(2))/857).

Programs

Magma

(1208787 +678878*Sqrt(2))/857^2; // G. C. Greubel, Apr 08 2018

Mathematica

RealDigits[(1208787+678878Sqrt[2])/857^2,10,120][[1]] (* Harvey P. Dale, Nov 09 2012 *)

PARI

(1208787 +678878*sqrt(2))/857^2 \\ G. C. Greubel, Apr 08 2018

Formula

Equals (1394 +487*sqrt(2))/(1394 -487*sqrt(2));

Equals (3+2*sqrt(2))*(42-5*sqrt(2))^2/(42+5*sqrt(2))^2.