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 A113476 Decimal expansion of 1/3*(log(2) + Pi/sqrt(3)). 8
 8, 3, 5, 6, 4, 8, 8, 4, 8, 2, 6, 4, 7, 2, 1, 0, 5, 3, 3, 3, 7, 1, 0, 3, 4, 5, 9, 7, 0, 0, 1, 1, 0, 7, 6, 6, 7, 8, 6, 5, 2, 2, 1, 2, 7, 4, 8, 4, 3, 3, 1, 9, 4, 3, 2, 3, 0, 1, 8, 8, 3, 1, 4, 9, 6, 0, 5, 0, 5, 6, 0, 1, 0, 3, 2, 0, 1, 6, 1, 9, 9, 7, 6, 3, 3, 2, 9, 4, 3, 8, 4, 0, 2, 8, 2, 6, 2, 8, 5, 4, 6, 6, 0, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This number is transcendental - this follows from a result of Baker (1968) on linear forms of algebraic numbers. REFERENCES Jolley, Summation of Series, Dover (1961), eq (79) page 16. Murray R. Spiegel, Seymour Lipschutz, John Liu. Mathematical Handbook of Formulas and Tables, 3rd Ed. Schaum's Outline Series. New York: McGraw-Hill (2009): p. 135, equation 21.16 LINKS Ivan Panchenko, Table of n, a(n) for n = 0..1000 A. Baker, Linear forms in the logarithms of algebraic numbers (IV). Mathematika, 15 (1968) pp. 204-216 L. Euler, De fractionibus continuis observationes, The Euler Archive, Index Number 123, Section 5 FORMULA Equals int_{0}^{1}dx/(1+x^3) = sum(k>=0, (-1)^k/(3k+1)) = 1 - 1/4 + 1/7 - 1/10 + 1/13 - 1/16 + ... (see A016777). - Benoit Cloitre, Alonso del Arte, Jul 29 2011 Generalized continued fraction: 1/(1 + 1^2/(3 + 4^2/(3 + 7^2/(3 + 10^2/(3 + ... ))))) due to Euler. For a sketch proof see A024217. - Peter Bala, Feb 22 2015 EXAMPLE 0.835648848264721053337... = A073010 + A193535. MATHEMATICA RealDigits[(Log[2]+\[Pi]/Sqrt[3])/3, 10, 120][[1]]  (* Harvey P. Dale, Mar 26 2011 *) PROG (PARI) 1/3*(log(2)+Pi/sqrt(3)) CROSSREFS Cf. A073010, A193535, A024217, A193534. Sequence in context: A196654 A019728 A265183 * A171043 A124599 A005601 Adjacent sequences:  A113473 A113474 A113475 * A113477 A113478 A113479 KEYWORD cons,nonn AUTHOR Benoit Cloitre, Jan 08 2006 STATUS approved

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Last modified December 11 07:47 EST 2019. Contains 329914 sequences. (Running on oeis4.)