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 A014537 Number of books required for n book-lengths of overhang in the harmonic book stacking problem. Sum_{i=1..a(n)} 1/i >= 2n and Sum_{i=1..a(n)-1} 1/i < 2n. 5
 4, 31, 227, 1674, 12367, 91380, 675214, 4989191, 36865412, 272400600, 2012783315, 14872568831, 109894245429, 812014744422, 6000022499693, 44334502845080, 327590128640500, 2420581837980561, 17885814992891026 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Bisection of A002387. - Robert G. Wilson v, Jan 24 2017 REFERENCES R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 259. LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..1000 (terms 1..350 from Alois P. Heinz). Mike Paterson and Uri Zwick, Overhang, arXiv:0710.2357 [math.HO], 2007. Eric Weisstein's World of Mathematics, Book Stacking Problem FORMULA a(n) = A002387(2n), n>=1. Least a(n) with H(a(n)) > 2n with the harmonic numbers H(k):= A001008(k)/A002805(k). MATHEMATICA f[n_] := (k = Floor[ N [ E^(n - EulerGamma) + 1/(2n), 24]] - 2; While[ Floor[ N[ Log[k] + EulerGamma + 1/(2k) - 1/(12k^2) + 1/(120k^4), 24]] < n, k++ ]; k); Table[ f[n], {n, 2, 32, 2} ] a[n_] := k /. FindRoot[ HarmonicNumber[k] == 2*n, {k, Exp[2*n]}, WorkingPrecision -> 100] // Ceiling; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jun 25 2013 *) CROSSREFS Cf. A002387. Sequence in context: A299663 A005216 A124033 * A136284 A183911 A039765 Adjacent sequences:  A014534 A014535 A014536 * A014538 A014539 A014540 KEYWORD nonn,nice AUTHOR EXTENSIONS More terms from Robert G. Wilson v, Dec 06 2001 Title corrected by Jeremy Tan, Sep 12 2020 STATUS approved

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Last modified April 22 19:11 EDT 2021. Contains 343177 sequences. (Running on oeis4.)