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A156057 Decimal expansion of log(3)/2. 1
5, 4, 9, 3, 0, 6, 1, 4, 4, 3, 3, 4, 0, 5, 4, 8, 4, 5, 6, 9, 7, 6, 2, 2, 6, 1, 8, 4, 6, 1, 2, 6, 2, 8, 5, 2, 3, 2, 3, 7, 4, 5, 2, 7, 8, 9, 1, 1, 3, 7, 4, 7, 2, 5, 8, 6, 7, 3, 4, 7, 1, 6, 6, 8, 1, 8, 7, 4, 7, 1, 4, 6, 6, 0, 9, 3, 0, 4, 4, 8, 3, 4, 3, 6, 8, 0, 7, 8, 7, 7, 4, 0, 6, 8, 6, 6, 0, 4, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Culler and Shalen abstract: We give lower bounds on the maximal injectivity radius for a closed orientable hyperbolic 3-manifold M with first Betti number 2, under some additional topological hypotheses. A corollary of the main result is that if M has first Betti number 2 and contains no fibroid surface then its maximal injectivity radius exceeds 0.32798. For comparison, Andrew Przeworski showed, with no topological restrictions, that the maximal injectivity radius exceeds arcsinh(1/4) = 0.247..., while the authors showed that if M has first Betti number at least 3 then the maximal injectivity exceeds log(3)/2 = 0.549.... The proof combines a result due to Przeworski with techniques developed by the authors in the 1990s.

Also decimal expansion of arctanh(1/2) = arccoth(2) = integral_{x>2} 1/(x^2-1). [Jean-Fran├žois Alcover, Jun 04 2013]

LINKS

Table of n, a(n) for n=1..99.

Marc Culler, Peter B. Shalen, Betti numbers and injectivity radii,

MATHEMATICA

RealDigits[Log[3]/2, 10, 120][[1]] (* Harvey P. Dale, Apr 13 2016 *)

CROSSREFS

Cf. A002391 (decimal expansion of natural logarithm of 3).

Sequence in context: A097943 A241420 A077142 * A125057 A021186 A195705

Adjacent sequences:  A156054 A156055 A156056 * A156058 A156059 A156060

KEYWORD

nonn,cons,easy

AUTHOR

Jonathan Vos Post, Feb 03 2009

EXTENSIONS

All digits were wrong. Corrected by N. J. A. Sloane, Feb 05 2009

STATUS

approved

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Last modified September 24 18:54 EDT 2017. Contains 292433 sequences.