A023493 a(n) = b(n) + d(n), where b(n) = (n-th Lucas number > 1) and d(n) = (n-th nonLucas number).

5, 9, 13, 19, 27, 39, 59, 89, 137, 214, 338, 538, 862, 1384, 2228, 3593, 5801, 9373, 15152, 24502, 39630, 64107, 103711, 167791, 271474, 439236, 710680, 1149885, 1860533, 3010385, 4870884, 7881234, 12752082, 20633279, 33385323