%I #8 Sep 08 2022 08:45:44
%S 4,6,8,7,7,8,8,3,6,6,9,2,2,9,7,1,9,6,1,1,6,7,2,9,9,1,7,1,1,5,5,5,3,3,
%T 4,3,0,7,0,7,1,8,5,8,3,8,3,3,5,9,3,0,0,9,2,9,2,2,0,8,8,2,0,2,6,5,1,1,
%U 7,2,2,2,6,0,9,5,6,6,9,3,7,1,1,6,5,8,8,4,3,9,7,9,6,3,9,9,3,1,6,9,2,6,9,0,6
%N Decimal expansion of (278307+179662*sqrt(2))/337^2.
%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A129999.
%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A159574.
%H G. C. Greubel, <a href="/A159576/b159576.txt">Table of n, a(n) for n = 1..10000</a>
%F Equals (626+287*sqrt(2))/(626-287*sqrt(2)).
%F Equals (3+2*sqrt(2))*(26-sqrt(2))^2/(26+sqrt(2))^2.
%e (278307+179662*sqrt(2))/337^2 = 4.68778836692297196116...
%t RealDigits[(278307+179662*Sqrt[2])/337^2, 10, 100][[1]] (* _G. C. Greubel_, May 05 2018 *)
%o (PARI) (278307+179662*sqrt(2))/337^2 \\ _G. C. Greubel_, May 05 2018
%o (Magma) (278307+179662*Sqrt(2))/337^2; // _G. C. Greubel_, May 05 2018
%Y Cf. A129999, A159574, A002193 (decimal expansion of sqrt(2)), A159575 (decimal expansion of (339+26*sqrt(2))/337).
%K cons,nonn
%O 1,1
%A _Klaus Brockhaus_, Apr 16 2009