A157216 Decimal expansion of (18 + 5*sqrt(2))/(18 - 5*sqrt(2)).

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, 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, 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

Offset: 1

Author

Klaus Brockhaus, Feb 25 2009

Keywords

• cons
• nonn

Comments

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

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

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for algebraic numbers, degree 2.

Crossrefs

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

Programs

Magma

(18+5*Sqrt(2))/(18-5*Sqrt(2)) // G. C. Greubel, Jan 27 2018

Mathematica

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

PARI

(18+5*sqrt(2))/(18-5*sqrt(2)) \\ G. C. Greubel, Jan 27 2018