A159892 - OEIS

%I #9 Sep 08 2022 08:45:44

%S 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,

%T 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,

%U 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

%N Decimal expansion of (450483+287918*sqrt(2))/439^2.

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

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

%H G. C. Greubel, <a href="/A159892/b159892.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%t RealDigits[N[(450483+287918*Sqrt[2])/439^2,300]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Mar 21 2011*)

%o (PARI) (450483+287918*sqrt(2))/439^2 \\ _G. C. Greubel_, May 17 2018

%o (Magma) (450483 +287918*Sqrt(2))/439^2; // _G. C. Greubel_, May 17 2018

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

%K cons,nonn

%O 1,1

%A _Klaus Brockhaus_, Apr 30 2009