A058336 a(n) = least value such that sequence increases and pairwise differences are unique.

1, 5, 6, 8, 14, 24, 35, 49, 61, 81, 103, 120, 153, 181, 219, 243, 288, 324, 398, 449, 489, 576, 639, 704, 792, 900, 952, 983, 1069, 1211, 1355, 1496, 1660, 1753, 1941, 2065, 2166, 2296, 2432, 2595, 2788, 2942, 3119, 3321, 3454, 3666, 3928, 3986, 4408, 4502