【Analysis】First, find the common multiple of 17 and 20 to determine the cycle of the sequence, then calculate how many numbers are in each cycle, which will help us find the 289th number.

【Solution】Solution: According to the analysis, multiples of 17 and 20 alternate, and the least common multiple of 17 and 20 is 340. It is easy to see that 1 to 340 forms one cycle, and each cycle contains $17+20-1$ numbers. $289=36 \times 8+1 \therefore$ the 289th number in the sequence is: $340 \times 8+17=2737$. Therefore, the answer is: 2737
4. (10 points) Write on the blackboard in ascending order all non-zero natural numbers that can be divided by 17 or 20; 17, $20,34,40,51,60, \cdots$ Then the number in the 289th position of this sequence is $\qquad$ .