OFFSET
1,2
COMMENTS
Note that one can do "better" in terms of projections if one groups the bricks asymmetrically into lozenges with holes. See the Ainsley and Drummond references. Ainsley considers only the case of four bricks, but achieves an overhang of (15 - 4*sqrt(2))/8, compared with 25/24 for the harmonic pile. - D. G. Rogers, Aug 31 2005
Lim_{n -> inf} a(n)/a(n-1) = exp(2). - Robert G. Wilson v, Jan 26 2017
REFERENCES
N. J. A. Sloane, Illustration for sequence M4299 (=A007340) in The Encyclopedia of Integer Sequences (with Simon Plouffe), Academic Press, 1995.
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..1000
S. Ainley, Finely Balanced, Math. Gaz., 63 (1979), 272.
J. E. Drummond, On stacking bricks to achieve a large overhang, Math. Gaz., 65 (1981), 40-42.
Eric Weisstein's World of Mathematics, Book Stacking Problem
EXAMPLE
Obviously a(1)=1. If the center of gravity of one brick is placed at the end of a second brick, the length of the stack of 2 bricks is 1.5. If the c.g. of that stack is placed at the end of a third brick, the length of the stack is 1.75. Continuing, we get a stack of length 1.916666... for 4 bricks and a stack of length 2.0416666... for 5 bricks. Thus a(2)=5.
MATHEMATICA
A002387[n_] := Floor[ Exp[n - EulerGamma] + 1/2]; a[n_] := A002387[2n - 2] + 1; a[1] = 1; Table[a[n], {n, 1, 20}] (* Jean-François Alcover, Dec 13 2011, after Charles R Greathouse IV *)
f[n_] := k /. FindRoot[HarmonicNumber[k -1] == 2n, {k, Exp[ 2n]}, WorkingPrecision -> 100] // Ceiling; Array[f, 21, 0] (* Robert G. Wilson v, Jan 26 2017 after Jean-François Alcover in A014537 *) (* note that the index is off by one *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John W. Layman, Nov 08 2001
EXTENSIONS
More terms from Vladeta Jovovic, Nov 14 2001
STATUS
approved