A self-generating sequence: there are a(n) (k+1)'s between successive k's, where k=5.

Terms

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