a(n) is the smallest number greater than a(n-1) whose name in US English contains n vowels.

Terms

a(0) =2a(1) =3a(2) =11a(3) =14a(4) =71a(5) =101a(6) =111a(7) =114a(8) =171a(9) =1071a(10) =1101a(11) =1111a(12) =1114a(13) =1171a(14) =11171a(15) =14171a(16) =71171a(17) =101171a(18) =111171a(19) =114171a(20) =171171a(21) =1071171a(22) =1101171a(23) =1111171a(24) =1114171a(25) =1171171a(26) =11171171a(27) =14171171a(28) =71171171a(29) =101171171