A100695 Largest denominator used in the Egyptian fraction representation of n/(n + 1) by the greedy algorithm.

2, 6, 4, 20, 3, 42, 24, 18, 15, 231, 12, 156, 231, 10, 240, 32640, 9, 342, 180, 126, 99, 34362, 8, 600, 312, 216, 168, 24360, 120, 633759288, 96, 88, 16728, 9240, 72, 6808, 5016, 6552, 60, 28536, 7, 1806, 924, 630, 483, 779730, 336, 294, 138075, 238, 79716

Offset

1,1

Comments

a(n) = A247765(n,A100678(n)). - Reinhard Zumkeller, Sep 25 2014

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000 (first 100 terms from Reinhard Zumkeller)

Index entries for sequences related to Egyptian fractions

Example

a(16) = 32640 because 16/17 = 1/2 + 1/3 + 1/10 + 1/128 + 1/32640.

Mathematica

a[n_] := Module[{m = n/(n+1)}, While[Numerator[m]>1, m = m-1/Ceiling[1/m]]; 1/m]; Array[a, 100] (* Jean-François Alcover, Mar 12 2019, after M. F. Hasler *)

Prog

(PARI) a(n)={n/=(n+1); while(numerator(n)>1, n-=1/ceil(1/n)); 1/n} \\ M. F. Hasler, Sep 24 2014
(Haskell)
a100695 = last . a247765_row -- Reinhard Zumkeller, Sep 25 2014

Crossrefs

Cf. A100678.

Cf. A247765.

Sequence in context: A333923 A063427 A066092 * A275121 A174824 A009262

Adjacent sequences: A100692 A100693 A100694 * A100696 A100697 A100698

Keyword

nonn

Author

John W. Layman, Dec 08 2004

Status

approved