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

1,2

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

Links

Table of n, a(n) for n=1..78.

Example

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,
  ...

Prog

(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

Crossrefs

Cf. A003506.

For numerators see A344008.

Sequence in context: A329380 A348146 A355076 * A130478 A308140 A306464

Adjacent sequences: A344004 A344005 A344006 * A344008 A344009 A344010

Keyword

nonn,tabl,frac

Author

Evan Lee, Jun 08 2021

Status

approved