A self-generating sequence: there are a(n) (k+1)'s between successive k's, where k=4.

Terms

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