This is an easy to memorize pattern: knit 2, purl 2, ending on a single knit stitch (so it's knit on a multiple of 4 + 1). This extra stitch creates the off-set pattern that has knit columns and purl columns separated by seed stitch columns. The result looks a bit like fisherman's rib. To make it symmetrical, you have to knit it on a multiple of 4 + 3, but that also changes the pattern from a one-row pattern to a two-row pattern. See: Scarf Stitch, Symmetrical. (On the swatch photos, the part before the casting off of 2 stitches is the asymmetric Scarf Stitch part.)

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