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A160584 Decimal expansion of (537 +92*sqrt(2))/521.

%I A160584 #10 Sep 08 2022 08:45:45
%S A160584 1,2,8,0,4,3,6,9,4,3,8,3,5,5,5,6,1,3,1,4,5,8,2,6,3,6,5,1,8,7,5,8,0,0,
%T A160584 8,1,2,3,3,8,5,9,8,4,8,8,5,5,0,2,4,8,0,2,8,2,7,6,8,8,0,1,0,7,2,8,4,3,
%U A160584 5,1,9,9,2,3,5,7,9,9,2,0,2,9,8,9,2,9,6,6,7,0,4,7,1,8,1,2,4,8,0,7,4,6,9,5,2
%N A160584 Decimal expansion of (537 +92*sqrt(2))/521.
%C A160584 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A129725.
%C A160584 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A160583.
%H A160584 G. C. Greubel, <a href="/A160584/b160584.txt">Table of n, a(n) for n = 1..10000</a>
%F A160584 Equals (23 +2*sqrt(2))/(23 -2*sqrt(2)).
%e A160584 (537 +92*sqrt(2))/521 = 1.28043694383555613145...
%p A160584 with(MmaTranslator[Mma]): Digits:=150:
%p A160584 RealDigits(evalf((537+92*sqrt(2))/521))[1]; # _Muniru A Asiru_, Apr 08 2018
%t A160584 RealDigits[(537 +92*Sqrt[2])/521, 10, 100][[1]] (* _G. C. Greubel_, Apr 07 2018 *)
%o A160584 (PARI) (537 +92*sqrt(2))/521 \\ _G. C. Greubel_, Apr 07 2018
%o A160584 (Magma) (537 +92*Sqrt(2))/521; // _G. C. Greubel_, Apr 07 2018
%Y A160584 Cf. A129725, A160583, A002193 (decimal expansion of sqrt(2)), A160585 (decimal expansion of (520659+314170*sqrt(2))/521^2).
%K A160584 cons,nonn
%O A160584 1,2
%A A160584 _Klaus Brockhaus_, Jun 08 2009