I knit socks on four (5 inch) double pointed needles, these days from the cuff down, and I enjoy socks with some amount of ribbing at the cuff.
Seems reasonable. I also tend to have two other restrictions:
Each needle should have the same number of stitches.
In the ribbing, each needle should begin with a knit stitch and end with a purl stitch.
This somewhat constrains the possibilities. Also given a preference for rubbings that are biased towards knit stitches, I tend to veto options that might otherwise be workable. Here's a quick cheat sheet of compliant patterns. Patterns are for one needle, repeat for each
12 stitches (48):
Knit 2, purl 2 till end.
Knit 3, purl 1 till end.
13 stitches (52): Knit 3, purl 2 twice; then knit 2, purl 1.
14 stitches (56): Knit 3, purl 2 twice; then knit 3, purl 1.
15 stitches (60):
Knit 3, purl 2 till end.
Knit 2, purl 1 till end.
16 stitches (64):
Knit 2, purl 2 till end.
Knit 3, purl 1 till end.
17 stitches (68): Knit 2, purl 2 twice; then knit 2, purl 1 three times.
18 stitches (72):
Knit 2, purl 1 till end.
Knit 3, purl 2 three times; then knit 2, purl 1.
19 stitches (76): Knit 3, purl 2 three times; then knit 3, purl 1.
20 stitches (80):
Knit 2, purl 2 till end.
Knit 3, purl 1 till end.
Knit 2, purl 1 till end.
Knit 3, purl 2 three times; then knit 2, purl 1.
21 stitches (84):
Knit 2, purl 1 till end.
Knit 3, purl 2 three times; then knit 2, purl 2.
22 stitches (88):
Knit 2, purl 1 six times, then knit 2, purl 2.
Knit 3, purl 3; then, knit 2, purl 2 till end..
23 stitches (96):
Knit 2, purl 2 five times; then knit 2, purl 1
Knit 3, purl 1 five times; then knit 2, purl 1
Knit 3, purl 2 four times; then knit 2, purl 1
24 stitches (100):
Knit 2, purl 2 till end.
Knit 3, purl 1 till end.
Knit 2, purl 1 till end.
Knit 3, purl 2 three times; then knit 2, purl 1.