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A261346 Decimal expansion of the side length median of a random triangle of unit inradius. 0
5, 5, 4, 8, 2, 0, 3, 9, 1, 8, 8, 7, 8, 4, 4, 5, 2, 7, 7, 6, 4, 4, 2, 9, 9, 7, 1, 8, 2, 1, 6, 9, 8, 8, 4, 9, 8, 9, 5, 0, 1, 4, 1, 1, 7, 0, 6, 4, 9, 4, 6, 9, 9, 7, 5, 2, 3, 7, 3, 2, 3, 3, 8, 4, 0, 7, 7, 0, 2, 5, 5, 2, 3, 4, 8, 6, 1, 5, 2, 8, 6, 1, 4, 0, 7, 4, 4, 9, 4, 7, 0, 0, 1, 6, 0, 6, 5, 6, 7, 0, 3, 4, 8, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..104.

Steven R. Finch, Three Random Tangents to a Circle, arXiv:1101.3931 (math.PR], 2011.

FORMULA

Side length density for x>2 is p(x) = (16/Pi^2)*((x*arctan((x + sqrt(x^2 - 4))/2) - x*arctan((x - sqrt(x^2 - 4))/2) + log((x + sqrt(x^2 - 4))/(x - sqrt(x^2 - 4))))/((x^2 + 4)*x)).

EXAMPLE

5.548203918878445277644299718216988498950141170649469975237323384077...

MATHEMATICA

digits = 104; p[x_] := (16/Pi^2)*((x*ArcTan[(x + Sqrt[x^2 - 4])/2] - x*ArcTan[(x - Sqrt[x^2 - 4])/2] + Log[(x + Sqrt[x^2 - 4])/(x - Sqrt[x^2 - 4])])/((x^2 + 4)*x)); P[x_?NumericQ] := NIntegrate[p[t], {t, 2, x}, WorkingPrecision -> digits + 5]; m = x /. FindRoot[P[x] == 1/2, {x, 5}, WorkingPrecision -> digits + 5]; First[RealDigits[m, 10, digits]]

CROSSREFS

Sequence in context: A094245 A117191 A011189 * A011409 A255240 A168578

Adjacent sequences:  A261343 A261344 A261345 * A261347 A261348 A261349

KEYWORD

cons,nonn

AUTHOR

Jean-Fran├žois Alcover, Aug 15 2015

STATUS

approved

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Last modified May 23 18:24 EDT 2017. Contains 286926 sequences.