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A014537
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Number of books required for n book-lengths of overhang in the harmonic book stapling problem. Sum (1/i,i=1..a(n)) >= 2n and Sum (1/i,i=1..a(n)-1) < 2n.
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2
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4, 31, 227, 1674, 12367, 91380, 675214, 4989191, 36865412, 272400600, 2012783315, 14872568831, 109894245429, 812014744422, 6000022499693, 44334502845080, 327590128640500, 2420581837980561, 17885814992891026
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 259.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..350
Mike Paterson and Uri Zwick, Overhang
Eric Weisstein's World of Mathematics, Book Stacking Problem
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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).
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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} ]
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CROSSREFS
| Sequence in context: A179562 A005216 A124033 * A136284 A183911 A039765
Adjacent sequences: A014534 A014535 A014536 * A014538 A014539 A014540
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KEYWORD
| nonn,nice
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 06 2001
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