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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).
5
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
1,3
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.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..247 (The first 31 rows)
EXAMPLE
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;
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 *)
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Leroy Quet, May 01 2005
EXTENSIONS
More terms from Jud McCranie, May 03 2005
STATUS
approved