A260618 Irregular triangle read by rows: denominators of the expansion of k/n using the greedy algorithm, 1<=k<=n.

1, 2, 1, 3, 2, 6, 1, 4, 2, 2, 4, 1, 5, 3, 15, 2, 10, 2, 4, 20, 1, 6, 3, 2, 2, 6, 2, 3, 1, 7, 4, 28, 3, 11, 231, 2, 14, 2, 5, 70, 2, 3, 42, 1, 8, 4, 3, 24, 2, 2, 8, 2, 4, 2, 3, 24, 1, 9, 5, 45, 3, 3, 9, 2, 18, 2, 6, 2, 4, 36, 2, 3, 18, 1, 10, 5, 4, 20, 3, 15, 2, 2, 10, 2, 5, 2, 4, 20, 2, 3, 15, 1, 11, 6, 66, 4, 44, 3, 33, 3, 9, 99, 2, 22, 2, 8, 88, 2, 5, 37, 4070, 2, 4, 15, 660, 2, 3, 14, 231, 1

Offset: 1

Author

Matthew Campbell, Sep 17 2015

Keywords

• nonn
• tabf

Examples

			Triangle begins ({} included for fraction separation):
  {1};
  {2}, {1};
  {3}, {2, 6}, {1};
  {4}, {2}, {2, 4}, {1};
  {5}, {3, 15}, {2, 10}, {2, 4, 20}, {1};
  {6}, {3}, {2}, {2, 6}, {2, 3}, {1};
  {7}, {4, 28}, {3, 11, 231}, {2, 14}, {2, 5, 70}, {2, 3, 42}, {1};
  {8}, {4}, {3, 24}, {2}, {2, 8}, {2, 4}, {2, 3, 24}, {1};
  {9}, {5, 45}, {3}, {3, 9}, {2, 18}, {2, 6}, {2, 4, 36}, {2, 3, 18}, {1};
  {10}, {5}, {4, 20}, {3, 15}, {2}, {2, 10}, {2, 5}, {2, 4, 20}, {2, 3, 15}, {1};
  {11}, {6, 66}, {4, 44}, {3, 33}, {3, 9, 99}, {2, 22}, {2, 8, 88}, {2, 5, 37, 4070}, {2, 4, 15, 660}, {2, 3, 14, 231}, {1};
		

Links

• Seiichi Manyama, Rows n=1..81 of triangle, flattened (Rows 1..29 from Andrew Howroyd)
• Wikipedia, Greedy algorithm for Egyptian fractions

Crossrefs

Cf. A050205, A050206, A050210, A098853, A100140.

Programs

PARI

rep(f)={L=List(); while(f<>0, my(t=ceil(1/f)); listput(L,t); f-=1/t); Vec(L)}
row(n)={concat(apply(k->rep(k/n), [1..n]))}
for(n=1, 11, print(row(n))) \\ Andrew Howroyd, Feb 26 2018