a(n) = Sum_{k=1..n} floor( 1/{k*sqrt(5)} ), where {x} := x - floor(x).

Terms

a(0) =4a(1) =6a(2) =7a(3) =8a(4) =13a(5) =15a(6) =16a(7) =17a(8) =25a(9) =27a(10) =28a(11) =29a(12) =43a(13) =46a(14) =47a(15) =48a(16) =124a(17) =128a(18) =130a(19) =131a(20) =132a(21) =137a(22) =139a(23) =140a(24) =141a(25) =148a(26) =150a(27) =151a(28) =152a(29) =164