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A160214 Decimal expansion of (1947891+1218490*sqrt(2))/953^2.

%I A160214 #14 Sep 08 2022 08:45:44
%S A160214 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 A160214 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 A160214 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 A160214 Decimal expansion of (1947891+1218490*sqrt(2))/953^2.
%C A160214 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A129975.
%C A160214 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A160212.
%H A160214 G. C. Greubel, <a href="/A160214/b160214.txt">Table of n, a(n) for n = 1..10000</a>
%F A160214 Equals (1690+721*sqrt(2))/(1690-721*sqrt(2)).
%F A160214 Equals (3+2*sqrt(2))*(31-2*sqrt(2))^2/(31+2*sqrt(2))^2.
%e A160214 (1947891+1218490*sqrt(2))/953^2 = 4.04212695934084840165...
%t A160214 RealDigits[(1947891 +1218490*Sqrt[2])/953^2, 10, 100][[1]] (* _G. C. Greubel_, Apr 08 2018 *)
%o A160214 (PARI) (1947891 +1218490*sqrt(2))/953^2 \\ _G. C. Greubel_, Apr 08 2018
%o A160214 (Magma) (1947891 +1218490*Sqrt(2))/953^2; // _G. C. Greubel_, Apr 08 2018
%Y A160214 Cf. A129975, A160212, A002193 (decimal expansion of sqrt(2)), A160213 (decimal expansion of (969+124*sqrt(2))/953).
%K A160214 cons,nonn
%O A160214 1,1
%A A160214 _Klaus Brockhaus_, May 18 2009