A050206 Triangle read by rows: smallest denominator of the expansion of k/n using the greedy algorithm, 1<=k<=n-1.

2, 3, 2, 4, 2, 2, 5, 3, 2, 2, 6, 3, 2, 2, 2, 7, 4, 3, 2, 2, 2, 8, 4, 3, 2, 2, 2, 2, 9, 5, 3, 3, 2, 2, 2, 2, 10, 5, 4, 3, 2, 2, 2, 2, 2, 11, 6, 4, 3, 3, 2, 2, 2, 2, 2, 12, 6, 4, 3, 3, 2, 2, 2, 2, 2, 2, 13, 7, 5, 4, 3, 3, 2, 2, 2, 2, 2, 2, 14, 7, 5, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 15, 8, 5, 4, 3, 3, 3, 2

Offset: 2

Author

Eric W. Weisstein

Keywords

• nonn
• easy
• tabl

Examples

			n\k | 1  2  3  4  5  6  7  8
----*------------------------
  2 | 2;
  3 | 3, 2;
  4 | 4, 2, 2;
  5 | 5, 3, 2, 2;
  6 | 6, 3, 2, 2, 2;
  7 | 7, 4, 3, 2, 2, 2;
  8 | 8, 4, 3, 2, 2, 2, 2;
  9 | 9, 5, 3, 3, 2, 2, 2, 2;
		

Links

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

Crossrefs

Cf. A050205, A050210 (Largest denominator), A260618.

Formula

T(n,k) = ceiling(n/k).

Extensions

Offset changed to 2 by Seiichi Manyama, Sep 18 2022