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User: Evan Lee

Evan Lee has authored 2 sequences.

A344008 Triangle of numerators corresponding to A344007.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 1, 3, 1, 3, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 2, 1, 4, 1, 1, 3, 1, 1, 1, 3, 1, 1, 2, 1, 4, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 5, 1, 4, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1

Offset: 1

Evan Lee, Jun 09 2021

			The triangle underlying A344007 begins:
  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 numerators are:
  1
  1, 1
  1, 1, 1
  1, 1, 1, 1
  2, 1, 1, 1, 1
  1, 2, 1, 1, 1, 1
  1, 3, 2, 1, 1, 1, 1
  3, 1, 3, 1, 2, 1, 1, 1
  1, 3, 1, 3, 1, 1, 2, 1, 1
  1, 1, 3, 1, 1, 3, 1, 1, 2, 1
  ...

Cf. A003506, A344007.

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(numerator, row); for (k=1, #drow, print1(drow[k], ", ")););} \\ Michel Marcus, Jun 09 2021

Corrected by Hugo Pfoertner and Michel Marcus, Jun 09 2021

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.

Original entry on oeis.org

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

Evan Lee, Jun 08 2021

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

			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,
  ...

Cf. A003506.

For numerators see A344008.

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

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User: Evan Lee

A344008 Triangle of numerators corresponding to A344007.

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