I tried your suggestion as well which was much easier using k rather than p. Both stitch patterns have a lovely web-like patterning to them, and I like the reversibility (which is why I was thinking of using it for scarves). I Googled it and sure enough, it is referred to as the Half F. Rib.
Thank you for teaching me something new!
Currently working on:
Two multi-coloured & multi-textures afghan
A children's ribbed sweater
A pair of slippers