A023498 a(n) = b(n) + d(n), where b(n) = (n-th Lucas number > 3) and d(n) = (n-th number that is 1 or 2 or is not a Fibonacci number).

5, 9, 15, 24, 36, 56, 86, 134, 211, 336, 536, 859, 1381, 2225, 3590, 5798, 9371, 15150, 24500, 39628, 64105, 103709, 167789, 271472, 439234, 710678, 1149883, 1860531, 3010384, 4870883, 7881233, 12752081, 20633278, 33385322