A023497 a(n) = b(n) + d(n), where b(n) = (n-th Lucas number > 3) and d(n) = (n-th number that is 1 or is not a Lucas number).

5, 9, 16, 24, 37, 56, 86, 135, 212, 336, 536, 859, 1381, 2226, 3591, 5799, 9371, 15150, 24500, 39628, 64105, 103709, 167789, 271473, 439235, 710679, 1149884, 1860532, 3010384, 4870883, 7881233, 12752081, 20633278, 33385322