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 A021016 Decimal expansion of 1/12. 7
 0, 8, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Multiplied by -1, this is zeta(-1) or zeta(-13), with zeta being the Riemann zeta function. Divided by 10, this is zeta(-3). - Alonso del Arte, Jan 05 2011 Multiplied by 10, this is 5/6, the resistance in ohm between opposite vertices of a cubical network when each edge has a resistance of 1 ohm. - Michel Marcus, Sep 02 2015 The variance of a continuous uniform distribution U(a,b) is (1/12)*(b-a)^2. - Jean-François Alcover, May 19 2016 5/6 is the Schnirelmann density of the sums of three squares and also the asymptotic density of the set of sums of three squares. See Wagstaff. - Michel Marcus, Apr 22 2020 -1/12 = zeta(-1) is the Ramanujan sum of 1 + 2 + 3 + .... [see facsimile] and was called "one of the most remarkable formulae in science" [Gannon]. - Peter Luschny, Jul 17 2020 REFERENCES Bruce C. Berndt, Ramanujan's Notebooks: Part 1, Springer-Verlag, 1985, pp. 135-136 Terry Gannon, Moonshine Beyond the Monster: The Bridge Connecting Algebra, Modular Forms and Physics, Cambridge University Press, 2010, p. 140. L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 40 (series n. 209) and p. 44 (series n. 239). LINKS Table of n, a(n) for n=0..98. Martin Gardner, The Five Platonic Solids, Mathematical Puzzles & Diversions. S. Ramanujan, Another way of finding the constant, Notebook 1, 1919. Samuel S. Wagstaff, Jr., The Schnirelmann Density of the Sums of Three Squares, Proc. Amer. Math. Soc. 52 (1975), 1-7. Wikipedia, 1 + 2 + 3 + 4 + .... Index entries for linear recurrences with constant coefficients, signature (1). FORMULA Equals 1/(1*3*5) + 1/(3*5*7) + 1/(5*7*9) + 1/(7*9*11) + ... = Sum_{i >= 0} 1/((2*i+1)*(2*i+3)*(2*i+5)), see Jolley in References. - Bruno Berselli, Mar 21 2014 Equals 1/(2*3*4) + 1/(3*4*5) + 1/(4*5*6) + 1/(5*6*7) + ... = Sum_{i > 0} 1/((i+1)*(i+2)*(i+3)). See Jolley in References, p. 48 (sum obtained from the series 268, case t = 2). - Bruno Berselli, Mar 29 2014 Equals 2*Pi*Integral_{z=-oo..oo} (z/(e^(-Pi*z) + e^(Pi*z)))^2. - Peter Luschny, Jul 17 2020 EXAMPLE 0.083333333333333333333333333333333333333333333333333333333333333333... MATHEMATICA RealDigits[1/12, 10, 100, -1][[1]] (* Bruno Berselli, Mar 21 2014 *) PROG (PARI) 1/12. \\ Michel Marcus, Mar 11 2018 CROSSREFS Cf. A005408 (odd numbers). Sequence in context: A010148 A246822 A168356 * A269296 A371502 A334363 Adjacent sequences: A021013 A021014 A021015 * A021017 A021018 A021019 KEYWORD nonn,cons,easy AUTHOR N. J. A. Sloane. STATUS approved

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Last modified August 12 04:50 EDT 2024. Contains 375085 sequences. (Running on oeis4.)