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

1,2

Comments

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

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..100 from Reinhard Zumkeller)

Wikipedia, Greedy algorithm for Egyptian fractions

Formula

a(n) >= A330808(n+1). Strict inequality holds when n+1 is in A396160. - Pontus von Brömssen, May 11 2026

Example

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

Prog

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

Crossrefs

Main diagonal of A050205.

Cf. A100695, A247765, A330808, A396160.

Sequence in context: A003434 A330808 A097849 * A396001 A026834 A071335

Adjacent sequences: A100675 A100676 A100677 * A100679 A100680 A100681

Keyword

nonn

Author

Pahikkala Jussi, Dec 06 2004

Extensions

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

Status

approved