a(n) is the least k such that 3^k begins with n!.

Terms

a(0) =0a(1) =0a(2) =3a(3) =8a(4) =5a(5) =805a(6) =1689a(7) =12317a(8) =197209a(9) =520852a(10) =4493819a(11) =16769097a(12) =2053077332a(13) =1110380591a(14) =39230711849a(15) =516641987008