A160205 - OEIS

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

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

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

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

%N Decimal expansion of (989043+524338*sqrt(2))/809^2.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A123654.

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

%H G. C. Greubel, <a href="/A160205/b160205.txt">Table of n, a(n) for n = 11..10000</a>

%F Equals (1282 +409*sqrt(2))/(1282 -409*sqrt(2)).

%F Equals (3+2*sqrt(2))*(29-4*sqrt(2))^2/(29+4*sqrt(2))^2.

%e (989043+524338*sqrt(2))/809^2 = 2.64418510371971670942...

%t RealDigits[(989043+524338*Sqrt[2])/809^2, 10, 100][[1]] (* _G. C. Greubel_, Apr 25 2018 *)

%o (PARI) (989043+524338*sqrt(2))/809^2 \\ _G. C. Greubel_, Apr 25 2018

%o (Magma) (989043+524338*Sqrt(2))/809^2; // _G. C. Greubel_, Apr 25 2018

%Y Cf. A123654, A160203, A002193 (decimal expansion of sqrt(2)), A160204 (decimal expansion of (873+232*sqrt(2))/809).

%K cons,nonn

%O 11,1

%A _Klaus Brockhaus_, May 18 2009