The maximums of the Erdos-Straus conjecture graph at the primes in S000342.
0, 1, 2, 5, 7, 9, 19, 32, 38, 63, 65, 104, 108, 148, 170, 192, 195, 240, 248, 310, 323, 421, 494, 555
1
T. D. Noe, Plot of 24 terms
Eric W. Weisstein, MathWorld: Erdős-Straus Conjecture
(Mma) Needs["`Egypt`”]; nn = 1000; t = Join[{0, 1}, Table[Length[EgyptianFraction[4/n, Method -> Lexicographic, MaxTerms -> 3, MinTerms -> 3, Duplicates -> Disallow, OutputFormat -> Plain]], {n, Prime[Range[3, nn]]}]]; t2 = {{2, 0}}; Do[If[t[[n]] > t2[[-1, 2]], AppendTo[t2, {Prime[n], t[[n]]}]], {n, 2, nn}]; Transpose[t2][[2]]
nonn
T. D. Noe, Nov 14 2014