A157216 - OEIS

%I #14 Feb 11 2025 15:12:50

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

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

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

%N Decimal expansion of (18 + 5*sqrt(2))/(18 - 5*sqrt(2)).

%C lim_{n -> infinity} b(n)/b(n-1) = (18+5*sqrt(2))/(18-5*sqrt(2)) for n mod 3 = {1, 2}, b = A129544.

%C lim_{n -> infinity} b(n)/b(n-1) = (18+5*sqrt(2))/(18-5*sqrt(2)) for n mod 3 = {0, 2}, b = A157213.

%H G. C. Greubel, <a href="/A157216/b157216.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.

%e (18 + 5*sqrt(2))/(18 - 5*sqrt(2)) = 2.29400890958816463059...

%t With[{c=5Sqrt[2]},RealDigits[(18+c)/(18-c),10,120][[1]]] (* _Harvey P. Dale_, Dec 13 2011 *)

%o (PARI) (18+5*sqrt(2))/(18-5*sqrt(2)) \\ _G. C. Greubel_, Jan 27 2018

%o (Magma) (18+5*Sqrt(2))/(18-5*Sqrt(2)) // _G. C. Greubel_, Jan 27 2018

%Y Cf. A129544, A157213, A157214 (decimal expansion of 18+5*sqrt(2)), A157215 (decimal expansion of 18-5*sqrt(2)).

%K cons,nonn,changed

%O 1,1

%A _Klaus Brockhaus_, Feb 25 2009