a(n) is the sum of the nonpowers of 2 in the 3x+1 sequence that starts at n.

Terms

a(0) =0a(1) =0a(2) =18a(3) =0a(4) =5a(5) =24a(6) =257a(7) =0a(8) =308a(9) =15a(10) =228a(11) =36a(12) =88a(13) =271a(14) =663a(15) =0a(16) =183a(17) =326a(18) =488a(19) =35a(20) =21a(21) =250a(22) =602a(23) =60a(24) =627a(25) =114a(26) =101409a(27) =299a(28) =411a(29) =693