A362289 a(n) is the largest denominator when the greedy algorithm for Egyptian fractions is applied to 1/n + 1/(n+1).

2, 3, 12, 180, 30, 1428, 56, 2520, 90, 2310, 132, 100292556, 182, 9240, 240, 119952, 306, 614444040, 380, 23100, 462, 42190274940, 552, 77390453400, 650, 201474, 756, 23370247110, 870, 200880, 992, 14523137084239067683872, 1122, 2206260, 1260, 104845560637757648698080

Offset: 1

Author

Sebastian F. Orellana, Apr 14 2023

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A050210.

Programs

Mathematica

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 *)

Formula

a(n) = A050210(n*(n+1), 2*n+1). - Michel Marcus, Apr 14 2023