I've seen many adjustable 317 configurations over the years, but this is a very weird one.
My understanding is that, as Alec_t has already mentioned, that a resistor between Out and Adjust terminals is mandatory. I never seen a *proven* configuration without one. If anybody has seen one that is proven to work, please let me know.
In National's original datasheet, there was a typical application for a 4 amp adjustable regulator, which consisted of a master and two slave LM317s.
The master had the resistor between Out and Adj, and the slaves had their Adj terminals connected to the master Adj terminal. Since all Outs were wired together via very low value resistors, in an indirect way the slaves also had a feedback resistance from Out and Adj.
And the overall feedback was controlled with a PNP and an opamp to adjust the voltage.