A160578 - OEIS

%I #13 Sep 08 2022 08:45:45

%S 1,7,3,7,3,7,8,6,7,5,9,8,6,9,9,2,5,8,7,2,8,2,8,4,5,2,4,6,1,3,0,1,4,4,

%T 9,3,2,0,2,8,6,1,8,2,7,6,4,3,8,4,5,2,9,9,8,2,7,3,0,6,1,6,0,3,8,6,9,0,

%U 5,3,9,2,7,5,8,3,4,5,7,1,6,9,9,9,2,3,3,5,2,2,1,9,2,4,3,1,2,4,3,0,8,5,4,4,8

%N Decimal expansion of (473+168*sqrt(2))/409.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A129641.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A160577.

%H G. C. Greubel, <a href="/A160578/b160578.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (42+8*sqrt(2))/(42-8*sqrt(2)).

%e (473+168*sqrt(2))/409 = 1.73737867598699258728...

%t RealDigits[(473+168Sqrt[2])/409,10,120][[1]] (* _Harvey P. Dale_, Mar 05 2015 *)

%o (PARI) (473 +168*sqrt(2))/409 \\ _G. C. Greubel_, Apr 08 2018

%o (Magma) (473 +168*Sqrt(2))/409; // _G. C. Greubel_, Apr 08 2018

%Y Cf. A129641, A160577, A002193 (decimal expansion of sqrt(2)), A160579 (decimal expansion of (204819+83570*sqrt(2))/409^2).

%K cons,nonn

%O 1,2

%A _Klaus Brockhaus_, Jun 08 2009