A160091 - OEIS

%I #8 Sep 08 2022 08:45:44

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

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

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

%N Decimal expansion of (587+102*sqrt(2))/569.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A101152.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A160090.

%H G. C. Greubel, <a href="/A160091/b160091.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (34+3*sqrt(2))/(34-3*sqrt(2)).

%e (587+102*sqrt(2))/569 = 1.28514900415124023721...

%t RealDigits[(587+102*Sqrt[2])/569, 10, 100][[1]] (* _G. C. Greubel_, Apr 15 2018 *)

%o (PARI) (587+102*sqrt(2))/569 \\ _G. C. Greubel_, Apr 15 2018

%o (Magma) (587+102*Sqrt(2))/569; // _G. C. Greubel_, Apr 15 2018

%Y Cf. A101152, A160090, A002193 (decimal expansion of sqrt(2)), A160092 (decimal expansion of (617139+371510*sqrt(2))/569^2).

%K cons,nonn

%O 1,2

%A _Klaus Brockhaus_, May 04 2009