The "Semi-Fibonacci sequence": a(1) = 1; a(n) = a(n/2) (n even); a(n) = a(n-1) + a(n-2) (n odd).

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =3a(5) =2a(6) =5a(7) =1a(8) =6a(9) =3a(10) =9a(11) =2a(12) =11a(13) =5a(14) =16a(15) =1a(16) =17a(17) =6a(18) =23a(19) =3a(20) =26a(21) =9a(22) =35a(23) =2a(24) =37a(25) =11a(26) =48a(27) =5a(28) =53a(29) =16