A160208 - OEIS

%I #13 Sep 08 2022 08:45:44

%S 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,

%T 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,

%U 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

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

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

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

%H G. C. Greubel, <a href="/A160208/b160208.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%t RealDigits[(1208787+678878Sqrt[2])/857^2,10,120][[1]] (* _Harvey P. Dale_, Nov 09 2012 *)

%o (PARI) (1208787 +678878*sqrt(2))/857^2 \\ _G. C. Greubel_, Apr 08 2018

%o (Magma) (1208787 +678878*Sqrt(2))/857^2; // _G. C. Greubel_, Apr 08 2018

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

%K cons,nonn

%O 1,1

%A _Klaus Brockhaus_, May 18 2009