Prime terms subtracted from Fibonacci terms (ignoring first two terms of Fibonacci sequence).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =2a(5) =8a(6) =17a(7) =36a(8) =66a(9) =115a(10) =202a(11) =340a(12) =569a(13) =944a(14) =1550a(15) =2531a(16) =4122a(17) =6704a(18) =10879a(19) =17640a(20) =28584a(21) =46289a(22) =74942a(23) =121304a(24) =196321a(25) =317710a(26) =514126a(27) =831933a(28) =1346160a(29) =2178196