A286720 Number of Egyptian fractions in the representation of 1-1/(2n+1) by the odd greedy expansion algorithm, without repeats.

4, 6, 6, 4, 6, 6, 4, 6, 6, 6, 8, 6, 6, 10, 6, 6, 8, 6, 12, 10, 10, 4, 6, 6, 6, 8, 6, 6, 8, 10, 6, 6, 8, 8, 6, 10, 6, 8, 6, 8, 6, 10, 6, 10, 6, 10, 6, 10, 6, 8, 8, 6, 8, 8, 8, 6, 6, 6, 10, 8, 6, 8, 10, 12, 8, 10, 6, 8, 8, 8, 10, 8, 6, 8, 10, 6, 8, 8, 6, 6, 8

Offset

1,1

Comments

The odd version of A100678.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Kevin Brown, Odd-Greedy Unit Fraction Expansions.

Wikipedia, Odd greedy expansion.

Example

For n = 1, 1-1/(2n+1) = 2/3 = 1/3 + 1/5 + 1/9 + 1/45 has 4 fractions in the representation, thus a(1) = 4.

Mathematica

odd[n_]:=If[OddQ[n], n, n+1]; a={}; For[n=0, n<100, n++; lst={}; k=2n/(2n+1); s1=0; While[k>0, s2=odd[Ceiling[1/k]]; If[s2==s1, s2+=2]; AppendTo[lst, s2]; k=k-1/s2; s1=s2]; a=AppendTo[a, Length[lst]]]; a

Crossrefs

Cf. A100678.

Sequence in context: A191761 A201451 A200352 * A201393 A327721 A327268

Adjacent sequences: A286717 A286718 A286719 * A286721 A286722 A286723

Keyword

nonn

Author

Amiram Eldar, May 30 2017

Status

approved