A105401 -id:A105401 - cp's OEIS frontend

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

Leroy Quet, May 01 2005

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.

			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;

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

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

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 *)

More terms from Jud McCranie, May 03 2005

A112330 a(n) is the number of terms in the n-th row of A106394.

Original entry on oeis.org

1, 2, 3, 3, 4, 5, 6, 5, 7, 8, 7, 6, 9, 7, 8, 8, 9, 8, 8, 9, 8, 11, 11, 11, 11, 9, 14, 10, 15, 12, 12, 15, 11, 14, 10, 14, 12, 13, 12, 16, 15, 13, 12, 12, 17, 13, 16, 16, 15, 16, 19, 14, 17, 16, 16, 21, 15, 18, 16, 18, 18, 18, 19, 21, 20, 19, 20, 22, 17, 20, 27, 19, 25, 20, 18, 23, 24

Offset: 1

Leroy Quet, Sep 04 2005

nonn

			H(4) = 1 + 1/2 + 1/3 + 1/4 = 25/12 has the Egyptian fraction expansion, by the greedy algorithm, of 1 + 1 + 1/12. Since there are 3 terms in this expansion, a(4) = 3.

Amiram Eldar, Table of n, a(n) for n = 1..142

Cf. A001008, A002805, A105401, A106394, A106395.

egyptFraction[f_] := Ceiling[1/Most[NestWhileList[# - 1/Ceiling[1/#] &, f, # != 0 &]]]; a[n_] := Length[egyptFraction[HarmonicNumber[n]]]; Array[a, 100] (* Amiram Eldar, Apr 09 2022 *)

More terms from David Wasserman, Apr 16 2009

cp's OEIS Frontend

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).

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