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

Author

John W. Layman, Dec 08 2004

Keywords

• nonn

Comments

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

Examples

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

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

Crossrefs

Cf. A100678.

Cf. A247765.

Programs

Haskell

a100695 = last . a247765_row -- Reinhard Zumkeller, Sep 25 2014

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 *)

PARI

a(n)={n/=(n+1);while(numerator(n)>1,n-=1/ceil(1/n));1/n} \\ M. F. Hasler, Sep 24 2014