A344007 Denominators of triangle formed by beginning with 1 on row 1, then producing row n by replacing the largest value on row n-1, k, by 1/n and k - 1/n, and arranging the entries in order from smallest to largest.

1, 2, 2, 6, 3, 2, 6, 4, 4, 3, 15, 6, 5, 4, 4, 12, 15, 6, 6, 5, 4, 12, 28, 15, 7, 6, 6, 5, 40, 12, 28, 8, 15, 7, 6, 6, 18, 40, 12, 28, 9, 8, 15, 7, 6, 18, 15, 40, 12, 10, 28, 9, 8, 15, 7, 77, 18, 15, 40, 12, 11, 10, 28, 9, 8, 15, 20, 77, 18, 15, 40, 12, 12, 11, 10, 28, 9, 8

Offset: 1

Author

Evan Lee, Jun 08 2021

Keywords

• nonn
• tabl
• frac

Comments

If there is more than one copy of the largest entry in row n-1, only one copy is changed.

For a somewhat similar triangle, see Leibniz's Harmonic Triangle A003506. - N. J. A. Sloane, Jun 09 2021

Examples

			The triangle's first 10 rows:
  1
  1/2,   1/2
  1/6,   1/3,   1/2
  1/6,   1/4,   1/4,   1/3
  2/15,  1/6,   1/5,   1/4,   1/4
  1/12,  2/15,  1/6,   1/6,   1/5,   1/4
  1/12,  3/28,  2/15,  1/7,   1/6,   1/6,   1/5
  3/40,  1/12,  3/28,  1/8,   2/15,  1/7,   1/6,   1/6
  1/18,  3/40,  1/12,  3/28,  1/9,   1/8,   2/15,  1/7,   1/6
  1/18,  1/15,  3/40,  1/12,  1/10,  3/28,  1/9,   1/8,   2/15,  1/7
  ...
The denominators are:
   1
   2,  2,
   6,  3, 2,
   6,  4, 4, 3,
  15,  6, 5, 4, 4,
  12, 15, 6, 6, 5, 4,
  ...
		

Crossrefs

Cf. A003506.

For numerators see A344008.

Programs

PARI

lista(nn) = {my(row, nrow, drow); for (n=1, nn, if (n==1, row = [1], k = vecmax(row); nrow = row; nrow[n-1] = 1/n; nrow = concat(nrow, k - 1/n); row = vecsort(nrow);); drow = apply(denominator, row); for (k=1, #drow, print1(drow[k], ", ")););} \\ Michel Marcus, Jun 09 2021