A157214 - OEIS

%I #13 Aug 21 2023 12:36:43

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

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

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

%N Decimal expansion of 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="/A157214/b157214.txt">Table of n, a(n) for n = 2..5000</a>

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

%F Equals 18 + 10*A010503. - _R. J. Mathar_, Feb 27 2009

%e 18+5*sqrt(2) = 25.07106781186547524400...

%t RealDigits[18+5Sqrt[2],10,150][[1]]  (* _Harvey P. Dale_, Mar 18 2011 *)

%o (PARI) 18 + 5*sqrt(2) \\ _G. C. Greubel_, Nov 28 2017

%o (Magma) [18 + 5*Sqrt(2)]; // _G. C. Greubel_, Nov 28 2017

%Y Cf. A129544, A157213, A157215 (decimal expansion of 18-5*sqrt(2)), A157216 (decimal expansion of (18-5*sqrt(2))/(18+5*sqrt(2))).

%K cons,nonn

%O 2,1

%A _Klaus Brockhaus_, Feb 25 2009