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A113476 Decimal expansion of 1/3*(log(2)+Pi/sqrt(3)). 5
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

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

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.

Sequence in context: A110234 A196654 A019728 * 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 November 23 11:48 EST 2014. Contains 249842 sequences.