Please don't build an LM317 based solution. Go for the LM723 and pass transistors suggested elsewhere in this thread.
An illustration why including a power supply design effort:
1. I want a 1.2-20v DC power supply with an LM317 that can shift an amp. Perfect spec.
2. Build an unregulated DC supply that shifts out the dropout voltage plus the max voltage plus a couple of volts to deal with capacitor ripple of 20+3+2 volts = 25v dc. An 18v AC transformer will do the job!
3. Whop the LM317 on the front end.
4. Think "hey i'll set this to 3.3v for an arduino project and I need 1A out - full whack"
Quite reasonable yes?
Well no it isn't.
The transformer isn't an 18v one. It's higher than that. More like 20v so it remains in spec when under load. So that's 28v DC.
The LM317 has to drop about 24v at half an amp. P=IE, so it has to shift 24W of power. The LM317 can shift, when well heatsunk with a bastard heatsink from hell just under half that. Bye bye regulator. They do explode as well. I've done it a couple of times.
The same story with a 2n3055 pass transistor is dissipation of 115W.
Hence LM723+2n3055 if you're going to do this. LM317 is only suitable for light loads. Not bench supplies, even your first one.
I haven't included mains transients here either which increase dissipation, dead short conditions etc. The LM723 has a programmable current limit so you can protect the rest of the circuit or the power supply in an overload condition.
Lots of design information here to explain this:
http://artofelectronics.net/wp-content/uploads/2016/02/AoE3_chapter9.pdfBut yes, DO build your own power supply. Just don't copy it from some idiots on the Internet. Learn about it then understand it, then build your own design confidently.