10 if it's the sequence of natural numbers
13 if it's the sequence of N such that N=2^n for natural numbers n, where N does not contain a 0
153 if it's sequence of N such that the the sum of the digits of N each raised to the power of the number of digits in N equals N.
However, i'm not sure that I understand your second example.
If N=2^n (assuming 2 to the power of n, not 2 xor n) then one would expect the sequence to be 1, 2, 4, 8, 16, etc.
If N=2^n using the C xor notation, then we would expect a sequence 3, 0, 1, 6, 7, 4, etc
Your third example is pure evil, and I'm glad that I never had you as a maths teacher ;-)
"Identify as many sequences as you can which fit this set of numbers, and tell me the next number in each sequence" is the non-trick actually being asked.
Someone recently pointed out to me that if you were designing hardware to (e.g.) refresh all memory locations in a system, or otherwise visit a set of 2^n sequential locations in no particular order, then using a maximal-length shift register of the appropriate width is actually simpler than a 'simple' adder or subtractor. That could be seen as a literal interpretation of Kolmogorov complexity.
11 if it's the sequence of N such that N=2^n for natural numbers n, where N does not contain a 24