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