Dyalog APL, 12 bytes

{⎕←2×⍵}⍣{0}1

Explanation:

• 1 starting from one,
• ⍣{0} forever
• {⎕←2×⍵} double it at each iteration, printing it

Dyalog APL, 12 10 bytes

-2 thanks to Adám

{⎕←2×⍵}⍣=1

Explanation:

• 1 starting from one,
• ⍣= until the last result and the current one are equal (never, so infinite loop)
• {⎕←2×⍵} double it at each iteration, printing it