Puzzles/Number sequences

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