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A160201 Decimal expansion of (1003+462*sqrt(2))/761.

%I A160201 #10 Sep 08 2022 08:45:44
%S A160201 2,1,7,6,5,6,5,9,2,0,9,1,5,0,7,2,1,5,8,4,0,5,2,3,0,2,1,1,0,1,8,2,3,9,
%T A160201 8,3,2,1,9,3,4,1,4,4,6,3,1,0,6,6,3,6,0,1,8,1,4,4,0,5,5,2,4,1,7,2,3,6,
%U A160201 7,7,2,7,3,3,8,9,6,1,0,3,1,7,9,3,5,4,5,2,0,9,0,4,8,5,3,7,5,0,4,1,5,2,9,0,0
%N A160201 Decimal expansion of (1003+462*sqrt(2))/761.
%C A160201 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A122694.
%C A160201 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A160200.
%H A160201 G. C. Greubel, <a href="/A160201/b160201.txt">Table of n, a(n) for n = 1..10000</a>
%F A160201 Equals (42 +11*sqrt(2))/(42 -11*sqrt(2)).
%e A160201 (1003+462*sqrt(2))/761 = 2.17656592091507215840...
%t A160201 RealDigits[(1003+462*Sqrt[2])/761,10,120][[1]] (* _Harvey P. Dale_, Feb 07 2016 *)
%o A160201 (PARI) (1003+462*sqrt(2))/761 \\ _G. C. Greubel_, Apr 25 2018
%o A160201 (Magma) (1003+462*Sqrt(2))/761; // _G. C. Greubel_, Apr 25 2018
%Y A160201 Cf. A122694, A160200, A002193 (decimal expansion of sqrt(2)), A160202 (decimal expansion of (591603+85478*sqrt(2))/761^2).
%K A160201 cons,nonn
%O A160201 1,1
%A A160201 _Klaus Brockhaus_, May 18 2009