Output "Fit" numbers

Bash + GNU utilities, 27

dc -e2o?p|tr -s 0|dc -e2i?p

Input read from STDIN.

05AB1E, 8 6 bytes

b00¬:C

Explanation

b        # convert input to binary
 00¬:    # replace 00 with 0 while possible
     C   # convert to int

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Saved 2 bytes thanks to Adnan

JavaScript (ES6), 41 bytes

n=>+`0b${n.toString(2).replace(/0+/g,0)}`