A self-generating sequence: there are a(n) (k+1)'s between successive k's, where k=3.

Terms

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