1,2

H(n) is the maximal distance that a stack of n cards can project beyond the edge of a table without toppling.

If n is not in {1,2,6} then a(n) has at least one prime factor other then 2 or 5 . E.g. a(5)=60 has a prime factor 3 and a(7)=140 has a prime factor 7. This implies that every H(n)=A001008(n)/A002805(n), n not from {1,2,6}, has an infinite decimal representation. For a proof see the J. Havil reference. - W. Lang, Jun 29 2007

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 259.

D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 1, p. 615.

J. Havil, Gamma, (in German), Springer, 2007, p. 35-6; Gamma: Exploring Euler's Constant, Princeton Univ. Press, 2003.

T. D. Noe, Table of n, a(n) for n=1..200

R. M. Dickau, Harmonic numbers and the book stacking problem

N. J. A. Sloane, Illustration of initial terms

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

H(n) = [ 1, 3/2, 11/6, 25/12, 137/60, 49/20, 363/140, 761/280, 7129/2520,... ] = A001008/A002805.

ZL:=n->sum(1/i, i=2..n): a:=n->floor(denom(ZL(n))): seq(a(n), n=1..29); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 28 2007

Denominator[ Drop[ FoldList[ #1 + 1/#2 &, 0, Range[ 30 ] ], 1 ] ] - Harvey P. Dale Feb 09 2000

Table[Denominator[HarmonicNumber[n]], {n, 1, 40}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 20 2006

Cf. A001008.

Cf. A075135.

Adjacent sequences: A002802 A002803 A002804 this_sequence A002806 A002807 A002808

Sequence in context: A083001 A119862 A111936 this_sequence A117481 A083268 A085911

nonn,easy,frac,nice

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 20 2006