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A160178 Decimal expansion of (755667+461578*sqrt(2))/617^2.

%I A160178 #10 Sep 08 2022 08:45:44
%S A160178 3,6,9,9,7,0,4,6,6,1,0,0,4,2,5,4,0,4,0,5,3,1,2,1,0,1,9,5,0,4,9,6,7,0,
%T A160178 5,1,7,6,9,3,0,0,4,0,1,3,4,9,3,2,7,3,8,7,3,7,4,1,4,1,4,8,5,5,9,6,4,5,
%U A160178 4,4,0,6,6,0,0,5,5,3,8,4,9,1,4,6,8,0,5,9,6,9,5,2,3,6,4,9,0,0,0,0,6,5,6,3,9
%N A160178 Decimal expansion of (755667+461578*sqrt(2))/617^2.
%C A160178 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A115135.
%C A160178 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A160176.
%H A160178 G. C. Greubel, <a href="/A160178/b160178.txt">Table of n, a(n) for n = 1..10000</a>
%F A160178 Equals (1066 +433*sqrt(2))/(1066 -433*sqrt(2)).
%F A160178 Equals (3 +2*sqrt(2))*(25 -2*sqrt(2))^2/(25 +2*sqrt(2))^2.
%e A160178 (755667+461578*sqrt(2))/617^2 = 3.69970466100425404053...
%t A160178 RealDigits[(755667+461578*Sqrt[2])/617^2,10,120][[1]] (* _Harvey P. Dale_, Oct 14 2017 *)
%o A160178 (PARI) (755667+461578*sqrt(2))/617^2 \\ _G. C. Greubel_, Apr 25 2018
%o A160178 (Magma) (755667+461578*Sqrt(2))/617^2; // _G. C. Greubel_, Apr 25 2018
%Y A160178 Cf. A115135, A160176, A002193 (decimal expansion of sqrt(2)), A160177 (decimal expansion of (633+100*sqrt(2))/617).
%K A160178 cons,nonn
%O A160178 1,1
%A A160178 _Klaus Brockhaus_, May 18 2009