The difference between each number and the next number is a power of 3: 1, 3, 9, 27. So to get the next number, just add the next power of 3 (81).
10
10
5
8
62
17?
6
The numbers are increasing by 1,4,9,16,25,36.... which are square numbers so the next increase is 49. Making the next number in the sequence 141
21. This is the Fibonacci series.
From the pattern (n + 4, n + 2, n + ?) I would say the next following number is 20 (n + 1).
A single number, such as 3773949588525642992, does not constitute a sequence.
34. Each number is the sum of the two preceding numbers. This is called the Fibonacci Sequence.