A160576 - OEIS

%I #15 Sep 08 2022 08:45:45

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

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

%U 2,2,9,4,1,9,6,3,5,2,1,2,5,3,1,5,9,0,6,9,7,1,4,6,3,0,7,3,1,5,6,0,0,6,6,2,9

%N Decimal expansion of (119187+47998*sqrt(2))/313^2.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A129640.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A160574.

%H G. C. Greubel, <a href="/A160576/b160576.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (932 +206*sqrt(2))/(932 -206*sqrt(2)).

%F Equals (3+2*sqrt(2))*(26-5*sqrt(2))^2/(26+5*sqrt(2))^2.

%e (119187+47998*sqrt(2))/313^2 = 1.90944505472939211538...

%t RealDigits[(119187 +47998*Sqrt[2])/313^2, 10, 100][[1]] (* _G. C. Greubel_, Apr 08 2018 *)

%o (PARI) (119187 +47998*sqrt(2))/313^2 \\ _G. C. Greubel_, Apr 08 2018

%o (Magma) (119187 +47998*Sqrt(2))/313^2; // _G. C. Greubel_, Apr 08 2018

%Y Cf. A129640, A160574, A002193 (decimal expansion of sqrt(2)), A160575 (decimal expansion of (363+130*sqrt(2))/313).

%K cons,nonn

%O 1,2

%A _Klaus Brockhaus_, Jun 08 2009