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

Terms

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