A160214 - OEIS

%I #14 Sep 08 2022 08:45:44

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

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

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

%N Decimal expansion of (1947891+1218490*sqrt(2))/953^2.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A129975.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A160212.

%H G. C. Greubel, <a href="/A160214/b160214.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (1690+721*sqrt(2))/(1690-721*sqrt(2)).

%F Equals (3+2*sqrt(2))*(31-2*sqrt(2))^2/(31+2*sqrt(2))^2.

%e (1947891+1218490*sqrt(2))/953^2 = 4.04212695934084840165...

%t RealDigits[(1947891 +1218490*Sqrt[2])/953^2, 10, 100][[1]] (* _G. C. Greubel_, Apr 08 2018 *)

%o (PARI) (1947891 +1218490*sqrt(2))/953^2 \\ _G. C. Greubel_, Apr 08 2018

%o (Magma) (1947891 +1218490*Sqrt(2))/953^2; // _G. C. Greubel_, Apr 08 2018

%Y Cf. A129975, A160212, A002193 (decimal expansion of sqrt(2)), A160213 (decimal expansion of (969+124*sqrt(2))/953).

%K cons,nonn

%O 1,1

%A _Klaus Brockhaus_, May 18 2009