This is the predecessor tree (presented as a general tree) for (3*n+3j)/2i for j=12 built to contain the paths to all the odd integers from 1 to 201. The complete paths are traced only to the extent that branches determining each path have been negotiated. At that point a parenthesized number indicates the number of steps to the odd integer in question. Only the path to 21 requires branching at every level until it is reached. When the odd number in question is 0[3], the paths continuing to leaf nodes are not shown; such path continuations (with smallest i) are listed at the end of the presentation of the tree.
The levels in the tree are column aligned up to the point where indication of branching was abandoned . The root is near the bottom at the extreme left. A forward slash (/) indicates that the parent appears in a line below its appearance and a back slash (\) indicates that the parent appears in a line above its appearance. Where the branching is dense the tree is easy to follow, but where children are well separated from their parents careful attention to the column alignment is required to make the proper associations. Note the number of children (high degree of branching) sometimes utilized in this small sample, e.g. those of 59049, with 5, right near the top.
/ 102789 --(7)-->91
/ 6561
\ 942597 --(5)-->63
/ 137781
/ 124659 --(8)-->185
/ 452709
\ 426465 --(7)-->159
/ 59049
/ 185895 --(4)-->189
/ 544563
/ 21 yes!
/ 33219
/ 315549
\ 664317 --(2)-->7
/ 184761
/ 271431
/ 672867
\ 1275021
\ 1082565
\ 2342277 --(8)-->201 (what about 73??)
/ 172773 --(7)-->187
/ 32805
/ 248103 --(4)-->177
/ 673353 --(5)-->131
/ 637875
\ 1523853 --(5)-->59
\ 1222533
/ 242757 --(8)-->13
/ 19683
/ 264627 --(7)-->53
\ 662661
\ 706401 --(6)-->87
\ 1502469 --(7)-->141
/ 14337 --(4)-->3
/ 143613
\ 588789 --(5)-->1
/ 120285
/ 111537
\ 417717w --(7)-->83
/ 400221 --(8)-->127
/ 216513
\ 977589 --(7)-->75
/ 295245
/ 229635 --(7)-->183
/ 182709 --(2)-->93
/ 67473
\ 1262277 --(3)-->31
/ 183465
/ 270459
/ 671409
\ 718065 --(6)-->137
/ 636417
\ 610173
\ 3077109 --(8)-->95
/ 177147
/ 45927 --(8)-->29
/ 64881 --(4)-->99
/ 181521
\ 306909 --(6)-->193
/ 269001
\ 540189 --(7)-->5
/ 334611
\ 715149 --(7)-->195
\ 767637
/ 535815 --(7)-->169
/ 1069443
\ 1248777 --(7)-->125
\ 1869885
/ 133407 --(7)-->173
/ 465831
/ 58131 --(2)-->33
/ 352917
/ 763965 --(3)-->11
/ 99387
/ 414801
\ 443961
/ 964467
\ 1108809 --(8)-->79
\ 1712421
/ 2630961 --(7)-->105
\ 2106081
/ 250047 --(6)-->145
/ 640791
\ 1531629 --(6)-->133
\ 1226907
/ 33237 --(1)-->117
/ 39447
\ 664389 --(2)-->39
/ 324891
/ 753057
/ 697653
/ 164025
/ 13365 --(4)-->57
/ 35721
\ 584901 --(5)-->19
/ 159651
/ 505197
/ 255879
/ 614547 --(3)-->81
\ 1187541
\ 1406241 --(6)-->69
/ 649539
/ 10935 --(7)-->67
/ 282123
\ 2832165 --(5)-->153
/ 741393 --(8)-->167
\ 688905
\ 1659933 --(8)-->191
/ 422091 --(6)-->147
/ 8988572
\ 1021329 --(7)-->115
/ 807003
\ 360855 --(8)-->163
/ 1476225
\ 1791153 --(7)-->9
/ 1240029
\ 3129597 --(10)-->97
/ 85293 --(8)-->179
/ 98415
\ 872613 --(8)-->77
/ 20763 --(2)-->51
/ 296865
\ 614493 --(3)-->17
/ 355509
/ 99873
/ 207765
/ 72171
/ 321489 --(8)-->41
/ 373977
\ 820125 --(5)-->135
/ 413343
/ 408969 --(4)-->27
/ 439587
\ 995085 --(7)-->113
\ 925101
\ 2027349 --(9)-->107
/ 2735937 --(9)-->109
/ 2184813
\ 5649021 --(9)-->175
/ 885735
/ 478953 --(7)-->111
/ 492075
\ 1135053 --(8)-->121
\ 1003833
/ 94041 --(7)-->55
/ 365229 --(7)-->139
/ 203391
\ 907605 --(6)-->165
/ 570807
\ 1345005 --(8)-->197
/ 1318761 --(9)-->143
/ 1121931
\ 5806485 --(9)-->151
/ 1948617
/ 3050865 --(9)-->37
\ 2421009
\ 6278877 --(7)-->45
/ 1594323
\ 4074381 --(11)-->61
\ 8325909
/ 3405159 --(9)-->47
\ 5373459
\ 6987465 --(9)-->119
/ 623295 --(8)-->149
/ 1200663
\ 1423737 --(8)-->157
/ 2066715
\ 2578473 --(9)-->199
/ 3365793
/ 2657205
/ 428675 --(9)-->171
\ 6908733
/ 801171 --(6)-->161
/ 1467477
\ 1779489 --(6)-->101
/ 308367
/ 793881 --(8)-->155
/ 728271
/ 220077 --(3)-->129
/ 148959
\ 1411749 --(4)-->43
/ 489159
/ 999459
\ 1764909
\ 3706965 --(8)-->35
/ 1358127
/ 2302911
\ 2893401 --(9)-->123
/ 3011499 --(11)-->181
/ 6200145 --(11)-->23
/ 4782969
\12577437 --(11)-->89
/ 3720087
\ 9743085 --(11)-->25
/ 9861183 --(10)-->49
/15057495
\19899513 --(9)-->15
/22851963
/34543665
/26040609
\ 19663317
/ 5845851
\15411789 --(14)-->85
\ 9034497
531441
\ 5491557
/ 1253151 --(8)-->71
/ 2145447
\ 2683449 --(8)-->103
\ 3483891
\11160261
\ 7263027 --(11)-->65
Since the odd integers from 1 to 201 are not necessarily leaf nodes, but the above predecessor tree stops at leaf nodes, I append a list of the remaining steps to leaf nodes for the sake of completeness. For 0[9], 2 or more steps are required; for 3[9] and 6[9], a single step suffices.
from steps to from steps to from steps to 3 84997 9 19461, 30437 15 150533 21 281605 27 117765, 136893, 187901 33 3077 39 35845 45 68613, 5821 51 101381 57 134149 63 166917, 45409 69 11269 75 27653 81 265221, 176481, 58161, 133045 87 60421 93 76805 99 93189, 71357 105 109573 111 125957 117 142341, 12641 123 158725 129 175109 135 7173, 128901, 166589 141 23557 147 23557 153 31749, 161509 159 39941 165 48133 171 56325, 123253 177 64517 183 72709 189 80901, 38589, 28661 195 89093 201 97285