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A101314 Decimal expansion of constant K, the unique solution > 1 to 2*Pi*log(k) == Pi*(1 - 1/k). 1
2, 8, 4, 6, 6, 8, 1, 3, 7, 0, 4, 0, 8, 3, 8, 4, 6, 1, 6, 8, 0, 2, 2, 5, 6, 7, 6, 7, 6, 9, 7, 1, 9, 1, 3, 0, 9, 8, 6, 5, 0, 2, 6, 7, 0, 5, 8, 5, 0, 4, 5, 4, 3, 1, 5, 1, 6, 9, 3, 1, 4, 7, 0, 9, 7, 7, 6, 6, 8, 9, 4, 3, 9, 0, 2, 5, 9, 2, 4, 4, 3, 7, 8, 3, 9, 6, 3, 7, 5, 5, 9, 8, 6, 0, 1, 1, 0, 7, 5, 0, 6, 3, 7, 4, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Decimal expansion of the number K > 1 such that the surface area equals the volume of Gabriel's horn from x=1 to x=K, where x is the radial (central) axis and Gabriel's horn is a function y=1/x rotated about the x-axis.

LINKS

Table of n, a(n) for n=0..104.

L. Bayon, P. Fortuny Ayuso, J.M. Grau, A.M. Oller-Marcen, M.M. Ruiz, The Best-or-Worst and the Postdoc problems, arXiv:1706.07185 [math.PR], 2017.

L Bayon, J Grau, AM Oller-Marcen, M Ruiz, PM Suarez, A variant of the Secretary Problem: the Best or the Worst, arXiv preprint arXiv:1603.03928, 2016

Eric Weisstein's World of Mathematics, "Gabriel's Horn."

FORMULA

-1/(2*ProductLog(-1, -1/(2*sqrt(e))))

EXAMPLE

0.2846681370408384616802256767697191309865026705850454315169314709776689439...

MATHEMATICA

RealDigits[ -1/(2*ProductLog[ -1, -1/(2*Sqrt[E])]), 10, 128][[1]]

CROSSREFS

Sequence in context: A222238 A019611 A138287 * A054530 A253883 A247445

Adjacent sequences:  A101311 A101312 A101313 * A101315 A101316 A101317

KEYWORD

cons,nonn

AUTHOR

Joseph Biberstine (jrbibers(AT)indiana.edu), Dec 23 2004

STATUS

approved

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Last modified January 23 13:40 EST 2020. Contains 331171 sequences. (Running on oeis4.)