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A160202 Decimal expansion of (591603+85478*sqrt(2))/761^2.

%I A160202 #11 Sep 08 2022 08:45:44
%S A160202 1,2,3,0,2,9,0,6,4,1,9,9,8,0,0,6,3,2,0,9,2,6,8,3,6,9,6,2,8,5,9,2,2,3,
%T A160202 8,4,5,0,3,4,0,7,4,7,6,6,0,0,4,8,0,8,6,1,0,6,3,4,0,4,0,6,0,7,4,7,9,2,
%U A160202 1,7,3,4,9,7,3,1,7,2,0,9,7,9,6,6,8,9,3,5,2,0,6,3,8,9,0,9,3,3,7,8,3,3,4,1,3
%N A160202 Decimal expansion of (591603+85478*sqrt(2))/761^2.
%C A160202 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A122694.
%C A160202 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A160200.
%H A160202 G. C. Greubel, <a href="/A160202/b160202.txt">Table of n, a(n) for n = 1..10000</a>
%F A160202 Equals (1082 +79*sqrt(2))/(1082 -79*sqrt(2)).
%F A160202 Eausl (3+2*sqrt(2))*(42-11*sqrt(2))^2/(42+11*sqrt(2))^2.
%e A160202 (591603+85478*sqrt(2))/761^2 = 1.23029064199800632092...
%t A160202 RealDigits[(591603+85478Sqrt[2])/761^2,10,120][[1]] (* _Harvey P. Dale_, Oct 25 2011 *)
%o A160202 (PARI) (591603+85478*sqrt(2))/761^2 \\ _G. C. Greubel_, Apr 25 2018
%o A160202 (Magma) (591603+85478*Sqrt(2))/761^2; // _G. C. Greubel_, Apr 25 2018
%Y A160202 Cf. A122694, A160200, A002193 (decimal expansion of sqrt(2)), A160201 (decimal expansion of (1003+462*sqrt(2))/761).
%K A160202 cons,nonn
%O A160202 1,2
%A A160202 _Klaus Brockhaus_, May 18 2009