|
%I #12 Sep 08 2022 08:45:44
%S 2,5,6,8,5,7,9,2,1,3,7,4,3,3,2,6,2,8,9,2,9,8,5,3,9,7,0,5,1,1,7,6,5,7,
%T 8,2,2,4,1,9,9,1,0,1,5,4,7,7,2,0,9,8,5,1,5,4,1,2,7,2,4,7,2,3,4,3,1,5,
%U 1,9,5,4,6,5,5,6,1,3,6,7,9,4,9,8,5,6,7,6,5,8,8,2,4,1,5,7,8,0,7,0,0,7,4,6,9
%N Decimal expansion of (3267 + 1702*sqrt(2))/47^2.
%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A118675.
%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A159750.
%H G. C. Greubel, <a href="/A159752/b159752.txt">Table of n, a(n) for n = 1..10000</a>
%F Equals (74 + 23*sqrt(2))/(74 - 23*sqrt(2)).
%F Equals (3 + 2*sqrt(2))*(7 - sqrt(2))^2/(7 + sqrt(2))^2.
%e (3267 + 1702*sqrt(2))/47^2 = 2.56857921374332628929...
%t RealDigits[(3267 +1702*Sqrt[2])/47^2, 10, 100][[1]] (* _G. C. Greubel_, May 22 2018 *)
%o (PARI) (3267 +1702*sqrt(2))/47^2 \\ _G. C. Greubel_, May 22 2018
%o (Magma) (3267 +1702*Sqrt(2))/47^2; // _G. C. Greubel_, May 22 2018
%Y Cf. A118675, A159750, A002193 (decimal expansion of sqrt(2)), A159751 (decimal expansion of (51+14*sqrt(2))/47).
%K cons,nonn
%O 1,1
%A _Klaus Brockhaus_, Apr 30 2009
|
