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 A195913 The denominator in a fraction expansion of log(2)-Pi/8. 6
 2, 3, 12, 30, 35, 56, 90, 99, 132, 182, 195, 240, 306, 323, 380, 462, 483, 552, 650, 675, 756, 870, 899, 992, 1122, 1155, 1260, 1406, 1443, 1560, 1722, 1763, 1892, 2070, 2115, 2256, 2450, 2499, 2652, 2862, 2915 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The minus sign in front of a fraction is considered the sign of the numerator and hence the sign of the fraction does not appear in this sequence. REFERENCES Granino A. Korn and Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company, New York (1968). LINKS Mohammad K. Azarian, Problem 1218, Pi Mu Epsilon Journal, Vol. 13, No. 2, Spring 2010, p. 116. Solution published in Vol. 13, No. 3, Fall 2010, pp. 183-185. FORMULA log(2) - Pi/8 = Sum_{n>=1} (-1)^(n+1)*(1/n) + (-1/2)*Sum_{n>=0} (-1)^n*(1/(2*n+1)). Empirical g.f.: x*(2+x+9*x^2+14*x^3+3*x^4+3*x^5) / ((1-x)^3*(1+x+x^2)^2). - Colin Barker, Dec 17 2015 From Bernard Schott, Aug 11 2019: (Start) k >= 1, a(3*k) = (4*k-1) * 4*k, k >= 0, a(3*k+1) = (4*k+1) * (4*k+2), k >= 0, a(3*k+2) = (4*k+1) * (4*k+3). The even terms a(3*k) and a(3*k+1) come from log(2) and the odd terms a(3*k+2) come from - Pi/8. (End) EXAMPLE 1/2 - 1/3 + 1/12 + 1/30 - 1/35 + 1/56 + 1/90 - 1/99 + 1/132 + 1/182 - 1/195 + 1/240 + ... = [(1 - 1/2) + (1/3 - 1/4) + (1/5 - 1/6) + (1/7 - 1/8) + (1/9 - 1/10) + (1/11 - 1/12) + ...] - (1/2)*[(1 - 1/3) + (1/5 - 1/7) + (1/9 - 1/11) + (1/13 - 1/15) + ... ] = log(2) - Pi/8. CROSSREFS Cf. A195909, A195697, A195947, A164833, A118324, A098289, A075549, A016655, A019675, A161685, A144981, A168056, A004772. Sequence in context: A228501 A089414 A260631 * A048085 A069062 A073618 Adjacent sequences:  A195910 A195911 A195912 * A195914 A195915 A195916 KEYWORD nonn,frac AUTHOR Mohammad K. Azarian, Sep 25 2011 STATUS approved

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Last modified May 30 15:21 EDT 2020. Contains 334726 sequences. (Running on oeis4.)