Puzzles/Number sequences

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The task is to find the hidden principle that constructs the list, and sometimes to continue the sequence, which is indicated by a question mark. Be aware: some sequences are infinite, some are finite. If you find a different solution than the given one please add it to the solution page. Creativity is encouraged!

Easy sequences[edit]

1 2 4 8 ?                  solution
1 2 4 7 ?                  solutions (more than one)
3 9 27 81 ?                solution
2 3 5 8 13 21 ?            solution
1 0 1 0 1 0 1 1 0 1 0 1    solution
2 3 6 7 1 9 4 5 8          solution
0 1 1 1 1 1 1 ...          solution

Medium Sequences[edit]

1 3 7 61 ?                 solution
2 -2 0 2 -3 0 ?            solution
1 4 1 5 9 ?                solution

Hard Sequences[edit]

                 ??
               85  90
             29  67   0    solution
           83  33  69   2
          1  81  91  57  36
       60  55  61  29  35   6
     29  42  45  23  13   5  16
   23  13  44   7  39  69  47  98
 61  41  91  82   1  37  27  71  36
6   4   6   9   0   8   9   5   9   6
                 ??
               73  94
             69  81  28    solution
           56   3  43  54
         33  98  49  91   8
        7  31  44  27  57   6
     26  45  71  38  61  65  88
   25  36   7  97  76  91  87  86
 83  55  98   1   5  10   1  15  96
3   9   3   4   4   3   0   7   5   6