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A098318 Decimal expansion of [5, 5, ...] = (5 + sqrt(29))/2. 12
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; text; 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

Table of n, a(n) for n=1..102.

A. Stakhov, Samuil Aranson, Hyperbolic Fibonacci and Lucas functions, Golden Fibonacci Goniometry, Bodnar's Geometry,..., Appl. Math. 2 (1) (2011) 74-84.

Wikipedia, Metallic mean

FORMULA

5 plus the constant in A085551. [From R. J. Mathar, 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 *)

PROG

(PARI) (5 + sqrt(29))/2 \\ Charles R Greathouse IV, Jul 24 2013

CROSSREFS

Cf. A001622, A014176, A098316, A098317, A010716 (continued fraction).

Sequence in context: A147326 A143114 A103133 * A293198 A193029 A094650

Adjacent sequences:  A098315 A098316 A098317 * A098319 A098320 A098321

KEYWORD

nonn,cons,easy

AUTHOR

Eric W. Weisstein, Sep 02 2004

STATUS

approved

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Last modified January 20 06:32 EST 2019. Contains 319325 sequences. (Running on oeis4.)