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

Author

Amiram Eldar, May 30 2017

Keywords

• nonn

Comments

The odd version of A100678.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Kevin Brown, Odd-Greedy Unit Fraction Expansions.
• Wikipedia, Odd greedy expansion.

Crossrefs

Cf. A100678.

Programs

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