A160579 - OEIS

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

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

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

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

%N Decimal expansion of (204819+83570*sqrt(2))/409^2.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A129641.

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

%H G. C. Greubel, <a href="/A160579/b160579.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (610+137*sqrt(2))/(610-137*sqrt(2)).

%F Equals (3+2*sqrt(2))*(42-8*sqrt(2))^2/(42+8*sqrt(2))^2.

%e (204819+83570*sqrt(2))/409^2 = 1.93091162419832230335...

%t RealDigits[(204819+83570*Sqrt[2])/409^2,10,120][[1]] (* _Harvey P. Dale_, Jul 16 2013 *)

%o (PARI) (204819 +83570*sqrt(2))/409^2 \\ _G. C. Greubel_, Apr 08 2018

%o (Magma) (204819 +83570*Sqrt(2))/409^2; // _G. C. Greubel_, Apr 08 2018

%Y Cf. A129641, A160577, A002193 (decimal expansion of sqrt(2)), A160578 (decimal expansion of (473+168*sqrt(2))/409).

%K cons,nonn

%O 1,2

%A _Klaus Brockhaus_, Jun 08 2009