A160092 - OEIS

%I #11 Sep 08 2022 08:45:44

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

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

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

%N Decimal expansion of (617139 + 371510*sqrt(2))/569^2.

%C Equals Lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A101152.

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

%H G. C. Greubel, <a href="/A160092/b160092.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (1940 + 766*sqrt(2))/(1940 - 766*sqrt(2)).

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

%e (617139+371510*sqrt(2))/569^2 = 3.52894104156222812994...

%t RealDigits[(617139 +371510*Sqrt[2])/569^2, 10, 100][[1]] (* _G. C. Greubel_, Apr 21 2018 *)

%o (PARI) (617139 +371510*sqrt(2))/569^2 \\ _G. C. Greubel_, Apr 21 2018

%o (Magma) (617139 +371510*Sqrt(2))/569^2; // _G. C. Greubel_, Apr 21 2018

%Y Cf. A101152, A160090, A002193 (decimal expansion of sqrt(2)), A160091 (decimal expansion of (587+102*sqrt(2))/569).

%K cons,nonn

%O 1,1

%A _Klaus Brockhaus_, May 04 2009