This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A362289 #30 Apr 15 2023 23:32:12 %S A362289 2,3,12,180,30,1428,56,2520,90,2310,132,100292556,182,9240,240,119952, %T A362289 306,614444040,380,23100,462,42190274940,552,77390453400,650,201474, %U A362289 756,23370247110,870,200880,992,14523137084239067683872,1122,2206260,1260,104845560637757648698080 %N A362289 a(n) is the largest denominator when the greedy algorithm for Egyptian fractions is applied to 1/n + 1/(n+1). %F A362289 a(n) = A050210(n*(n+1), 2*n+1). - _Michel Marcus_, Apr 14 2023 %e A362289 For n=16, 1/16 + 1/17 = 33/272 which written in Egyptian fractions is 1/9 + 1/98 + 1/119952 and the largest denominator is 119952. %t A362289 egyptFraction[f_] := Ceiling[1/Most[NestWhileList[# - 1/Ceiling[1/#] &, f, # != 0 &]]]; a[n_] := egyptFraction[1/n + 1/(n + 1)][[-1]]; Array[a, 40] (* _Amiram Eldar_, Apr 14 2023 *) %Y A362289 Cf. A050210. %K A362289 nonn %O A362289 1,1 %A A362289 _Sebastian F. Orellana_, Apr 14 2023