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A160585 Decimal expansion of (520659 +314170*sqrt(2))/521^2.

%I A160585 #13 Sep 08 2022 08:45:45
%S A160585 3,5,5,4,9,6,2,1,2,7,6,4,7,4,6,3,9,8,4,7,4,0,7,9,6,5,1,3,7,3,5,8,0,5,
%T A160585 7,3,8,0,5,8,1,1,8,7,5,5,4,0,9,7,4,1,9,9,2,3,6,6,3,6,1,2,8,3,9,7,9,0,
%U A160585 1,7,2,5,5,1,6,2,0,4,3,2,0,0,5,3,2,0,7,2,3,5,3,3,2,8,0,3,5,0,1,6,4,7,1,9,3
%N A160585 Decimal expansion of (520659 +314170*sqrt(2))/521^2.
%C A160585 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A129725.
%C A160585 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A160583.
%H A160585 G. C. Greubel, <a href="/A160585/b160585.txt">Table of n, a(n) for n = 1..10000</a>
%F A160585 Equals (890 +353*sqrt(2))/(890 -353*sqrt(2)).
%F A160585 Equals (3 +2*sqrt(2))*(23 -2*sqrt(2))^2/(23 +2*sqrt(2))^2.
%e A160585 (520659 +314170*sqrt(2))/521^2 = 3.55496212764746398474...
%p A160585 with(MmaTranslator[Mma]): Digits:=150:
%p A160585 RealDigits(evalf((520659+314170*sqrt(2))/521^2))[1]; # _Muniru A Asiru_, Apr 08 2018
%t A160585 RealDigits[(520659+314170Sqrt[2])/521^2,10,120][[1]] (* _Harvey P. Dale_, Aug 23 2011 *)
%o A160585 (PARI) (520659 +314170*sqrt(2))/521^2 \\ _G. C. Greubel_, Apr 07 2018
%o A160585 (Magma) (520659 +314170*Sqrt(2))/521^2; // _G. C. Greubel_, Apr 07 2018
%Y A160585 Cf. A129725, A160583, A002193 (decimal expansion of sqrt(2)), A160584 (decimal expansion of (537+92*sqrt(2))/521).
%K A160585 cons,nonn
%O A160585 1,1
%A A160585 _Klaus Brockhaus_, Jun 08 2009