|
| |
|
|
A098318
|
|
Decimal expansion of [5, 5, ...] = (5 + sqrt(29))/2.
|
|
5
| |
|
|
5, 1, 9, 2, 5, 8, 2, 4, 0, 3, 5, 6, 7, 2, 5, 2, 0, 1, 5, 6, 2, 5, 3, 5, 5, 2, 4, 5, 7, 7, 0, 1, 6, 4, 7, 7, 8, 1, 4, 7, 5, 6, 0, 0, 8, 0, 8, 2, 2, 3, 9, 4, 4, 1, 8, 8, 4, 0, 1, 9, 4, 3, 3, 5, 0, 0, 8, 3, 2, 2, 9, 8, 1, 4, 1, 3, 8, 2, 9, 3, 4, 6, 4, 3, 8, 3, 1, 6, 8, 9, 0, 8, 3, 9, 9, 1, 7, 7, 4, 2, 2, 0
(list; constant; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| The "metallic" constants A001622, A014176 etc. are defined inserting a= 1, 2, 3, 4,... etc into (a+sqrt(a^2+4))/2. [Stakhov & Aranson] - R. J. Mathar, Feb 14 2011
This is the length/width ratio of a 5-extension rectangle; see A188640 where the metallic constants are defined for rational numbers. [From Clark Kimberling, Apr 09 2011]
|
|
|
LINKS
| A. Stakhov, Samuil Aranson, Hyperbolic Fibonacci and Lucas functions, Golden Fibonacci Goniometry, Bodnar's Geometry,..., Appl. Math. 2 (1) (2011) 74-84.
|
|
|
FORMULA
| 5 plus the constant in A085551. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2008]
|
|
|
EXAMPLE
| 5.19258240...
|
|
|
MATHEMATICA
| r=5; t=(r+(4+r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120] (* Clark Kimberling, Apr 09 2011 *)
|
|
|
CROSSREFS
| Cf. A001622, A014176, A098316, A098317, A010716 (continued fraction).
Sequence in context: A147326 A143114 A103133 * A193029 A094650 A189234
Adjacent sequences: A098315 A098316 A098317 * A098319 A098320 A098321
|
|
|
KEYWORD
| nonn,cons,easy
|
|
|
AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Sep 02 2004
|
| |
|
|
