### Brain Teasers

# 3, 9, 33

Find the next three numbers in this sequence:

3, 9, 33, 129, 513, ?, ?, ?

3, 9, 33, 129, 513, ?, ?, ?

### Hint

bin### Answer

2049, 8193, 32769The numbers are the decimal form of the binary numbers when you take 11 (3), then add two 0's to the middle to get 1001 (9), and then add two more 0's to the middle to get 100001 (33) and so on:

11 = 3

1001 = 9

100001 = 33

10000001 = 129

1000000001 = 513

100000000001 = 2049

10000000000001 = 8193

1000000000000001 = 32769

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