Conway's "para-budding" sequence.

Terms

a(0) =1a(1) =3a(2) =2a(3) =5a(4) =8a(5) =5a(6) =9a(7) =5a(8) =10a(9) =15a(10) =9a(11) =15a(12) =21a(13) =13a(14) =20a(15) =11a(16) =19a(17) =27a(18) =16a(19) =25a(20) =13a(21) =23a(22) =33a(23) =19a(24) =30a(25) =41a(26) =25a(27) =37a(28) =20a(29) =33