# [Detour](https://rawgit.com/cyoce/detour/master/interp.html), 20 bytes
This one is going for the "infinite sequence" option.

    v1vq:$
      $+
    p,p^
    ^ q

[Try it online!](https://rawgit.com/cyoce/detour/master/interp.html?hex=djF2cTokCiAgJCsKcCxwXgpeIHE%3D)

Branch 1 takes a number, prints it, adds it with the number from Branch 2, then puts the result in Branch 2<br>
Branch 2 takes a number, feeds it to the addition with A, then puts the original number (*not* the sum) in Branch 1.

For a better explanation click the link and you'll see it in action.

More "readable" version:
# [Detour](https://rawgit.com/cyoce/detour/master/interp.html), 267 bytes

    :$v  1v   q   # split into branches
             
              +   # push sum of last 2 fibonacci numbers to branch 2
          {  
    
      p  ,p   ^   # print branch 1, merge with branch 3
    
          }
    
      ^   q       # push branch 2 into branch 1 for printing and recycling
    
    # 1   2   3

[Try it online!](https://rawgit.com/cyoce/detour/master/interp.html?hex=OiR2ICAxdiAgIHEgICAjIHNwbGl0IGludG8gYnJhbmNoZXMKICAgICAgICAgCiAgICAgICAgICArICAgIyBwdXNoIHN1bSBvZiBsYXN0IDIgZmlib25hY2NpIG51bWJlcnMgdG8gYnJhbmNoIDIKICAgICAgeyAgCgogIHAgICxwICAgXiAgICMgcHJpbnQgYnJhbmNoIDEsIG1lcmdlIHdpdGggYnJhbmNoIDMKCiAgICAgIH0KCiAgXiAgIHEgICAgICAgIyBwdXNoIGJyYW5jaCAyIGludG8gYnJhbmNoIDEgZm9yIHByaW50aW5nIGFuZCByZWN5Y2xpbmcKCiMgMSAgIDIgICAz)