I don’t have a pattern, so making the Oslo Hat as I see it.

Provisional crochet cast on 116 st. using 3.75mm hook onto 3.25mm needle.
join to knit in the round (Put the BOR marker).

Continue knitting in the round for 24cm.

Unravel the provisional cast on onto a spare needle.
Knit 2 tog. (live st. on the working needle and st. from provisional cast on) all the way around.
Knit for 6 rows. (those 6 rows will become the purl rows on the hat)
Turn the knitting direction by using German short rows.

Continue knitting in the round for another 18cm from the connection of the brim (50 rows).

Put markers every 29 stitches and start the decreases on every row.

At BOR, K1, K2tog, knit to two stitches before M, SSK, SM, K1, K2tog; repeat * to * twice; knit to two stitches before BOR, SSK. (8 stitches decreased)

There are only knit rows, no purling.