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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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A001008, A002805, A105401, A106395, A112330. Sequence in context: A136642 A080382 A349203 * A325530 A171712 A091412 Adjacent sequences: A106391 A106392 A106393 * A106395 A106396 A106397 KEYWORD easy,nonn,tabf AUTHOR Leroy Quet, May 01 2005 EXTENSIONS More terms from Jud McCranie, May 03 2005 STATUS approved

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Last modified August 11 05:00 EDT 2024. Contains 375059 sequences. (Running on oeis4.)