A160204 - OEIS

%I #10 Sep 08 2022 08:45:44

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

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

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

%N Decimal expansion of (873+232*sqrt(2))/809.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A123654.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A160203.

%H G. C. Greubel, <a href="/A160204/b160204.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (29+4*sqrt(2))/(29-4*sqrt(2)).

%e (873+232*sqrt(2))/809 = 1.48466940231218547753...

%t RealDigits[(873+232Sqrt[2])/809,10,120][[1]] (* _Harvey P. Dale_, Mar 22 2018 *)

%o (PARI) (873+232*sqrt(2))/809 \\ _G. C. Greubel_, Apr 25 2018

%o (Magma) (873+232*Sqrt(2))/809; // _G. C. Greubel_, Apr 25 2018

%Y Cf. A123654, A160203, A002193 (decimal expansion of sqrt(2)), A160205 (decimal expansion of (989043+524338*sqrt(2))/809^2).

%K cons,nonn

%O 1,2

%A _Klaus Brockhaus_, May 18 2009