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 A276813 Continued fraction for the ratio of the lowest two Dirichlet eigenvalues of the Laplacian within the regular pentagon. 1
 2, 1, 1, 8, 1, 4, 2, 2, 16, 3, 3, 1, 3, 1, 1, 2, 1, 1, 3, 1, 3, 3, 5, 1, 13, 1, 4, 1, 1, 13, 4, 3, 1, 4, 1, 1, 6, 5, 9, 1, 13, 2, 15, 1, 2, 3, 3, 1, 4, 9, 2, 14, 1, 4, 1, 7, 1, 1, 11, 1, 4, 5, 2, 3, 2, 1, 14, 1, 1, 2, 1, 1, 1, 1, 20, 3, 2, 1, 2, 2, 7, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The eigenvalues of the Laplacian within the regular pentagon with Dirichlet boundary conditions are calculated to at least 1000 digits. The ratio of the second eigenvalue to the first is calculated and expressed as a continued fraction. The ratio has an advantage since it is independent of the pentagon area. All terms in this expansion are correct. LINKS Robert Stephen Jones, Table of n, a(n) for n = 1..978 EXAMPLE 2.52683872... = 2+1/(1+1/(1+1/(8+1/(1+...)))). CROSSREFS Cf. A262823. Sequence in context: A060865 A078689 A230069 * A134470 A342992 A119418 Adjacent sequences:  A276810 A276811 A276812 * A276814 A276815 A276816 KEYWORD nonn,cofr AUTHOR Robert Stephen Jones, Sep 18 2016 STATUS approved

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Last modified May 11 02:34 EDT 2021. Contains 343784 sequences. (Running on oeis4.)