Dyalog APL, 12 bytes
{⎕←2×⍵}⍣{0}1
Explanation:
1
starting from one,⍣{0}
forever{⎕←2×⍵}
double it at each iteration, printing it
{⎕←2×⍵}⍣{0}1
Explanation:
1
starting from one,⍣{0}
forever{⎕←2×⍵}
double it at each iteration, printing it