login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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-Fran├žois 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

Eric W. Weisstein

EXTENSIONS

More terms from Robert G. Wilson v, Dec 06 2001

Title corrected by Jeremy Tan, Sep 12 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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