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A014537
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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.
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5
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4, 31, 227, 1674, 12367, 91380, 675214, 4989191, 36865412, 272400600, 2012783315, 14872568831, 109894245429, 812014744422, 6000022499693, 44334502845080, 327590128640500, 2420581837980561, 17885814992891026
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OFFSET
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1,1
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COMMENTS
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 259.
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LINKS
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Mike Paterson and Uri Zwick, Overhang, arXiv:0710.2357 [math.HO], 2007.
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FORMULA
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a(n) = A002387(2n), n>=1. Least a(n) with H(a(n)) > 2n with the harmonic numbers H(k):= A001008(k)/A002805(k).
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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