A157260 Decimal expansion of (7 + 2*sqrt(2))/(7 - 2*sqrt(2)).

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

Offset

1,1

Comments

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A129288.

Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A157257.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Index entries for algebraic numbers, degree 2.

Formula

Equals (57 + 28*sqrt(2))/41. - Klaus Brockhaus, May 01 2009

Example

(7 +2*sqrt(2))/(7 -2*sqrt(2)) = 2.35604828649869905771...

Mathematica

RealDigits[(7 + 2*Sqrt[2])/(7 - 2*Sqrt[2]), 10, 50][[1]] (* G. C. Greubel, Nov 28 2017 *)

Prog

(PARI) (7+2*sqrt(2))/(7-2*sqrt(2)) \\ G. C. Greubel, Nov 28 2017
(Magma) [(7+2*Sqrt(2))/(7-2*Sqrt(2))]; // G. C. Greubel, Nov 28 2017

Crossrefs

Cf. A129288, A157257, A157258 (decimal expansion of 7+2*sqrt(2)), A157259 (decimal expansion of 7-2*sqrt(2)).

Cf. A157300 (decimal expansion of (1683+58*sqrt(2))/41^2). - Klaus Brockhaus, May 01 2009

Sequence in context: A256301 A226609 A370730 * A336017 A291486 A177870

Adjacent sequences: A157257 A157258 A157259 * A157261 A157262 A157263

Keyword

cons,nonn

Author

Klaus Brockhaus, Feb 26 2009

Status

approved