A281530 Triangle read by rows: T(n,k) = number of terms for the shortest Egyptian fraction representation of k/n, 1 <= k < n.

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, 3, 3, 3

Offset: 2

Author

Arkadiusz Wesolowski, Jan 23 2017

Keywords

• nonn
• tabl

Comments

Not same as A050205. Example: the fraction 9/20 requires three terms in its greedy expansion, but 9/20 = 1/4 + 1/5, so T(20,9) = 2.

Examples

			The triangle T(n,k) begins:
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

• Index entries for sequences related to Egyptian fractions

Crossrefs

Cf. A281527.