A157123 Decimal expansion of (11 + 3*sqrt(2))/(11 - 3*sqrt(2)).

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

Offset: 1

Author

Klaus Brockhaus, Feb 25 2009

Keywords

• cons
• nonn

Comments

Lim_{n -> infinity} b(n)/b(n-1) = (11+3*sqrt(2))/(11-3*sqrt(2)) for n mod 3 = {1, 2}, b = A157119.

Lim_{n -> infinity} b(n)/b(n-1) = (11+3*sqrt(2))/(11-3*sqrt(2)) for n mod 3 = {0, 2}, b = A157120.

Examples

			(11 + 3*sqrt(2))/(11 - 3*sqrt(2)) = 2.25570966132644925457...
		

Links

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

Crossrefs

Cf. A157119, A157120, A157121 (decimal expansion of 11+3*sqrt(2)), A157122 (decimal expansion of 11-3*sqrt(2)).

Programs

Magma

(11+3*Sqrt(2))/(11-3*Sqrt(2)) // G. C. Greubel, Jan 27 2018

Mathematica

RealDigits[(11 + 3*Sqrt[2])/(11 - 3*Sqrt[2]), 10, 100][[1]] (* G. C. Greubel, Jan 27 2018 *)

PARI

(11+3*sqrt(2))/(11-3*sqrt(2)) \\ G. C. Greubel, Jan 27 2018