a(n)=least k such that base 3 representation of n begins as s(k), where s=A003137.

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =1a(5) =9a(6) =2a(7) =8a(8) =15a(9) =3a(10) =21a(11) =20a(12) =5a(13) =6a(14) =33a(15) =1a(16) =7a(17) =42a(18) =34a(19) =9a(20) =2a(21) =23a(22) =11a(23) =8a(24) =13a(25) =40a(26) =69a(27) =15a(28) =77a(29) =81