A101314 Decimal expansion of constant K, the unique solution > 1 to 2*Pi*log(k) == Pi*(1 - 1/k).

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

Offset: 0

Author

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

Keywords

• cons
• nonn

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.

Examples

			0.2846681370408384616802256767697191309865026705850454315169314709776689439...
		

Links

• L. Bayon, P. Fortuny Ayuso, J. M. Grau, A. M. Oller-Marcen, and M.M. Ruiz, The Best-or-Worst and the Postdoc problems, arXiv:1706.07185 [math.PR], 2017.
• L. Bayon, J. Grau, A. M. Oller-Marcen, M. Ruiz, and P. M. Suarez, A variant of the Secretary Problem: the Best or the Worst, arXiv preprint arXiv:1603.03928 [math.PR], 2016.
• Eric Weisstein's World of Mathematics, Gabriel's Horn.

Programs

Mathematica

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

Formula

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