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).

%I A106394 #21 Apr 09 2022 06:34:33
%S A106394 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,
%T A106394 56,1,1,2,4,13,489,5339880,1,1,2,3,11,212,113013,18448242120,1,1,1,51,
%U A106394 3711,30680205,1192281609186360,1,1,1,10,312,180180
%N 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).
%C A106394 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
%C A106394 The n-th row of the table has A112330(n) terms.
%H A106394 Amiram Eldar, <a href="/A106394/b106394.txt">Table of n, a(n) for n = 1..247</a> (The first 31 rows)
%e A106394 By the greedy algorithm, Sum_{k=1..4} 1/k = 1 + 1 + 1/12.
%e A106394 Table begins:
%e A106394   1;
%e A106394   1, 2;
%e A106394   1, 2,  3;
%e A106394   1, 1, 12;
%e A106394   1, 1,  4, 30;
%e A106394   1, 1,  3,  9, 180;
%t A106394 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 *)
%Y A106394 Cf. A001008, A002805, A105401, A106395, A112330.
%K A106394 easy,nonn,tabf
%O A106394 1,3
%A A106394 _Leroy Quet_, May 01 2005
%E A106394 More terms from _Jud McCranie_, May 03 2005