The numbers n where records occur in S000581.
0, 3, 11, 38, 83, 167, 227, 398, 668, 902, 908, 1238, 1448, 1592, 2273, 2672, 3167, 3632, 3713, 5297, 6368, 8153, 8777, 14528, 14852, 16673, 19697, 21188, 25472, 32612, 35108, 48158, 58775, 59408, 60143, 66692, 67262, 75983, 84752, 97583, 101888, 114743
1
T. D. Noe, Plot of 89 terms
T. D. Noe, Table of 89 terms
(Mma) lim = 10000; ps = Join[{0}, Prime[Range[PrimePi[lim]]]]; sq = Range[0, Sqrt[lim]]^2; s = Select[Flatten[Table[i + j, {i, ps}, {j, sq}]], # <= lim &]; z = Complement[Range[lim], Union[s]]; za = Table[{i, 0}, {i, z}]; t = Transpose[Sort[Join[za, Tally[s]]]][[2]]; mx = 0; t2 = {}; Do[If[t[[i]] > mx, mx = t[[i]]; AppendTo[t2, i - 1]], {i, Length[t]}]; t2
Cf. S000581.
nonn,hard
T. D. Noe, Apr 20 2015