A050205 Triangle read by rows: number of terms in unit fraction representation of k/n using the greedy algorithm, 1<=k<=n-1.

1, 1, 2, 1, 1, 2, 1, 2, 2, 3, 1, 1, 1, 2, 2, 1, 2, 3, 2, 3, 3, 1, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 3, 3, 1, 1, 2, 2, 1, 2, 2, 3, 3, 1, 2, 2, 2, 3, 2, 3, 4, 4, 4, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 1, 2, 3, 3, 3, 3, 2, 3, 3, 3, 3, 4, 1, 1, 2, 2, 2, 3, 1, 2, 2, 3, 3, 3, 4, 1, 2, 1, 2, 1, 2, 3, 2, 2, 2, 3

Offset: 2

Author

Eric W. Weisstein

Keywords

• nonn
• easy
• tabl

Examples

			2/3 = 1/2 + 1/6. So T(3,2) = 2.
n\k | 1  2  3  4  5  6  7  8
----*------------------------
  2 | 1;
  3 | 1, 2;
  4 | 1, 1, 2;
  5 | 1, 2, 2, 3;
  6 | 1, 1, 1, 2, 2;
  7 | 1, 2, 3, 2, 3, 3;
  8 | 1, 1, 2, 1, 2, 2, 3;
  9 | 1, 2, 1, 2, 2, 2, 3, 3;
		

Links

• Seiichi Manyama, Rows n = 2..141, flattened
• Eric Weisstein's World of Mathematics, Unit Fraction.
• Wikipedia, Greedy algorithm for Egyptian fractions.

Crossrefs

Cf. A050206, A050210 (Largest denominator), A260618.

Extensions

Offset changed to 2 by Seiichi Manyama, Sep 18 2022