a(2n) = n+2, a(2n-1) = smallest number requiring n+2 letters in English.

Terms

a(0) =1a(1) =3a(2) =4a(3) =4a(4) =3a(5) =5a(6) =11a(7) =6a(8) =15a(9) =7a(10) =13a(11) =8a(12) =17a(13) =9a(14) =24a(15) =10a(16) =23a(17) =11a(18) =73a(19) =12a(20) =3000a(21) =13a(22) =11000a(23) =14a(24) =15000a(25) =15a(26) =101a(27) =16a(28) =104a(29) =17