A100678 Number of Egyptian fractions in the representation of n/(n+1) via the greedy algorithm.

1, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, 4, 3, 4, 5, 3, 4, 4, 4, 4, 5, 3, 4, 4, 4, 4, 5, 4, 6, 4, 4, 5, 5, 4, 5, 5, 5, 4, 5, 3, 4, 4, 4, 4, 5, 4, 4, 5, 4, 5, 5, 4, 5, 4, 5, 5, 5, 4, 5, 6, 4, 5, 5, 5, 6, 5, 5, 4, 6, 5, 5, 5, 5, 5, 5, 4, 5, 6, 6, 5, 6, 4, 5, 6, 5, 6, 6, 5, 4, 5, 5, 5, 5, 5

Offset: 1

Author

Pahikkala Jussi, Dec 06 2004

Keywords

• nonn

Comments

a(n) = length of n-th row in table A247765. - Reinhard Zumkeller, Sep 25 2014

Examples

			a(16) = 5 because 16/17 = 1/2 + 1/3 + 1/10 + 1/128 + 1/32640.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..100 from Reinhard Zumkeller)
• Wikipedia, Greedy algorithm for Egyptian fractions

Crossrefs

Cf. A100695.

Cf. A247765.

Programs

Haskell

a100678 = length . a247765_row -- Reinhard Zumkeller, Sep 25 2014

PARI

A100678(n)={ my(x = n/(n+1), nb = 1); while(x -= 1/ceil(1/x), nb++); nb} \\ Michel Marcus, Aug 12 2013, minor edits by M. F. Hasler, Sep 25 2014

Extensions

More terms from M. F. Hasler, Sep 25 2014