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

Author

Klaus Brockhaus, Apr 30 2009

Keywords

• cons
• nonn

Comments

lim_{n -> infinity} b(n)/b(n-1) = (450483+287918*sqrt(2))/439^2 for n mod 3 = 0, b = A130645.

lim_{n -> infinity} b(n)/b(n-1) = (450483+287918*sqrt(2))/439^2 for n mod 3 = 1, b = A159890.

Examples

			(450483+287918*sqrt(2))/439^2 = 4.45027028944088490751...
		

Links

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

Crossrefs

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

Programs

Magma

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

Mathematica

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

PARI

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

Formula

Equals (802 +359*sqrt(2))/(802 -359*sqrt(2)).

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