Description of the first IC

I believe it is a phase-shift oscillator that worked at about 1.3 MHz. Kilby first demonstrated a flip-flop built entirely with semiconductor elements, but it was not a monolithic part—it was assembled from individual elements.

The first IC was a phase-shift oscillator. From Kilby's own account:

The history of Kilby's ICs can be found here.

The IC is a phase-shift oscillator. Excerpts (emphasis mine):

He sketched in his notebook the complete circuit of a phase-shift oscillator on a bar of germanium.

Within two weeks, the first three oscillators were completed and ready to test. What TI managers saw on that historic day of September 12, 1958, was a tiny bar of germanium, measuring 7/16-x1/16-inches, with protruding wires, glued to a glass slide. It was a rough device by anyone's standards. But when Kilby applied the voltage, an unending sine wave undulated across the oscilloscope screen.

Here is another, more general account of that story.