Each number in the sequence has two possible successors, so if we just look at
what values can succeed each other without regard to their position in the sequence, n, 
we get a binary tree.

However, since n can only be prime when it is congruent to +/-1 mod 6, some
otherwise potential successors can never be reached.

The transition from single digits, to double digits always occurs with a(n)=11,
and n can either be congruent to -1 or 1 mod 6, so we get the following two trees,
shown below and continuing until the branches transition either to 3 digits or back to 1 digit...

n mod 6
-----------------------------------------
   1      11
   2      21      
   3      22
   4      42_______________________
   5*     44                     34
   0      54___________          53______
   1*     55         95          45    95
   2      65         69          64    69    
   3      66         [7]         56    [7]
   4      86______               75___________
   5*     78    98               67         97
   0      [8]   99__________     86______   89______
   1*           [1]    [101]     78    98   [9]   79
   2                             [8]   99         [8]
   3                                   [1]

n mod 6
-----------------------------------------
   5      11
   0      21__________________________
   1*     22                        32
   2      42                        33
   3      44                        43	
   4      54____________            44__________________
   5*     55          95            54                74
   0      65______    69_______     55______          57____________
   1*     66    76    [7]    17     65    95          85          95
   2      86    77           81     66    69          68          69
   3      78    87           28     86    [7]         96          [7]
   4      [8]   88______     [3]    78______          89______
   5*           [9]   98            [8]   97          [9]   79
   0                  99________          89______          [8]
   1*                 [1]  [101]          [9]   79
   2                                            [8]

Both of these trees can transition to 101, but 101 always occurs when n is congruent to 1 mod 6,
so we only get 1 tree of three digits numbers for 101.

n mod 6
-----------------------------------------
   1      101
   2      201
   3      202
   4      302_______________
   5*     303            703
   0      403_______     407_______
   1*     404    904     804    904
   2      504    509     508    509
   3      505    [15]    [15]   [15]
   4      605_______________
   5*     606            706
   0      806_______     707_______
   1*     708    908     807    907
   2      [17]   909     808    809
   3             [19]    [18]   [18]

Now we are left with four cases for transitioning back to 2 digits from 3 digits...

18 and 19 will immediately transition all the way back to 1 digit, as the next position will be congruent to 4 mod 6,
and the in both cases, the next composite is 20, which backwards is 2.

17 gives us the tree...

n mod 6
-----------------------------------------
   2      17
   3      81
   4      28______
   5*     [3]   92
   0            39______
   1*           [4]   14
   2                  51
   3                  25
   4                  62____________
   5*                 36          76
   0                  83______    77______
   1*                 48    98    87    97
   2                  94    99    88    89
   3                  59    [1]   [9]   [9]
   4                  [6]

and 15 gives us...

n mod 6
-----------------------------------------
   3     15
   4     61___________________
   5*    26                 76
   0     72______           77______
   1*    47    37           87    97
   2     84    83           88    89
   3     58    48           [9]   [9]
   4     [6]   94______
   5*          59    79
   0           [6]   [8]

Therefore the transitions into 3 digit are always followed very soon
by transitions back to 2 digits and soon after back to 1 digit.

Thus the highest number reachable is 909, which appears in the tree shown above for 101.