a(n) is the smallest positive integer > a(n-1) with exactly n letters when spelled in English.

Terms

a(0) =1a(1) =4a(2) =7a(3) =11a(4) =15a(5) =18a(6) =21a(7) =24a(8) =27a(9) =73a(10) =101a(11) =104a(12) =107a(13) =111a(14) =115a(15) =118a(16) =121a(17) =124a(18) =127a(19) =173a(20) =323a(21) =373a(22) =1104a(23) =1107a(24) =1111a(25) =1115a(26) =1118a(27) =1121a(28) =1124a(29) =1127