A106394 Table read by rows, where n-th row is denominators of Egyptian fraction, derived using the greedy algorithm, of the n-th harmonic number (Sum_{k=1..n} 1/k).

1, 1, 2, 1, 2, 3, 1, 1, 12, 1, 1, 4, 30, 1, 1, 3, 9, 180, 1, 1, 2, 11, 514, 395780, 1, 1, 2, 5, 56, 1, 1, 2, 4, 13, 489, 5339880, 1, 1, 2, 3, 11, 212, 113013, 18448242120, 1, 1, 1, 51, 3711, 30680205, 1192281609186360, 1, 1, 1, 10, 312, 180180

Offset: 1

Author

Leroy Quet, May 01 2005

Keywords

• easy
• nonn
• tabf

Comments

Let s be the sum of the harmonic numbers. When s > 1, the Egyptian fraction here begins with floor(s) 1's. - Jud McCranie, May 03 2005

The n-th row of the table has A112330(n) terms.

Examples

			By the greedy algorithm, Sum_{k=1..4} 1/k = 1 + 1 + 1/12.
Table begins:
  1;
  1, 2;
  1, 2,  3;
  1, 1, 12;
  1, 1,  4, 30;
  1, 1,  3,  9, 180;
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..247 (The first 31 rows)

Crossrefs

Cf. A001008, A002805, A105401, A106395, A112330.

Programs

Mathematica

egyptFraction[f_] := Ceiling[1/Most[NestWhileList[# - 1/Ceiling[1/#] &, f, # != 0 &]]]; row[n_] := egyptFraction[HarmonicNumber[n]]; Table[row[n], {n, 1, 12}] // Flatten (* Amiram Eldar, Apr 09 2022 *)

Extensions

More terms from Jud McCranie, May 03 2005