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A090388 Decimal expansion of 1 + sqrt(3). 13
2, 7, 3, 2, 0, 5, 0, 8, 0, 7, 5, 6, 8, 8, 7, 7, 2, 9, 3, 5, 2, 7, 4, 4, 6, 3, 4, 1, 5, 0, 5, 8, 7, 2, 3, 6, 6, 9, 4, 2, 8, 0, 5, 2, 5, 3, 8, 1, 0, 3, 8, 0, 6, 2, 8, 0, 5, 5, 8, 0, 6, 9, 7, 9, 4, 5, 1, 9, 3, 3, 0, 1, 6, 9, 0, 8, 8, 0, 0, 0, 3, 7, 0, 8, 1, 1, 4, 6, 1, 8, 6, 7, 5, 7, 2, 4, 8, 5, 7, 5, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

1 + sqrt(3) is the length of the minimal Steiner network that connects the four vertices of a unit square. - Lekraj Beedassy, May 02 2008

This is the case n = 12 in the identity (Gamma(1/n)/Gamma(3/n))*(Gamma((n-1)/n)/Gamma((n-3)/n)) = 1 + 2*cos(2*Pi/n). - Bruno Berselli, Dec 14 2012

Equals n + n/(n + n/(n + n/(n + ...))) for n = 2. - Stanislav Sykora, Jan 23 2014

A non-optimal solution to the problem of finding the length of shortest fence that protects privacy of a square garden [Kawohl]. Cf. A256965. - N. J. A. Sloane, Apr 14 2015

REFERENCES

Bernd Kawohl, Some nonconvex shape optimization problems, in: Optimal Shape Design, Eds. A.Cellina u. A. Ornelas, Springer Lecture Notes in Math.1740 (2000), p. 7-46. (http://www.mi.uni-koeln.de/mi/Forschung/Kawohl/kawohl/publikationsliste.html, item 58)

Ian Stewart, Pursuing Polygonal Privacy, Mathematical Recreations Column, Scientific American, 284 (No. 2, 2001), 88-89.

LINKS

Table of n, a(n) for n=1..101.

MATHEMATICA

RealDigits[1 + Sqrt[3], 10, 100][[1]] (* Alonso del Arte, Feb 23 2014 *)

CROSSREFS

Cf. n + n/(n + n/(n + ...)): A090458 (n = 3), A090488 (n = 4), A090550 (n = 5), A092294 (n = 6), A092290 (n = 7), A090654 (n = 8), A090655 (n = 9), A090656 (n = 10). - Stanislav Sykora, Jan 23 2014

Cf., also A256965.

Sequence in context: A197281 A019703 A124910 * A021370 A248140 A088538

Adjacent sequences:  A090385 A090386 A090387 * A090389 A090390 A090391

KEYWORD

easy,nonn,cons

AUTHOR

Felix Tubiana (fat2(AT)columbia.edu), Feb 05 2004

EXTENSIONS

Better definition from Rick L. Shepherd, Jul 02 2004

STATUS

approved

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Last modified July 8 00:21 EDT 2015. Contains 259363 sequences.