a(n)=least k such that base 4 representation of n begins at s(k), where s=A030399.

Terms

a(0) =2a(1) =1a(2) =5a(3) =2a(4) =16a(5) =9a(6) =12a(7) =10a(8) =1a(9) =6a(10) =4a(11) =21a(12) =13a(13) =5a(14) =29a(15) =18a(16) =110a(17) =2a(18) =112a(19) =17a(20) =16a(21) =59a(22) =84a(23) =9a(24) =14a(25) =48a(26) =36a(27) =85a(28) =12a(29) =53