Overlapping Leaves stitch - Very beautiful!! I think it would be lovely in a scarf, just add 4 to 6 sts of garter stitch to each edge so the reverse stockinette doesn't roll.

Knitted in a multiple of 15 sts, + 2 and 20-row repeat.
Row 1 - RS: P2, * k13, p2; rep from * to end.
Row 2: K2, * p13, k2; rep from * to end.
Row 3: P2, * k10, k2tog, yo, k1, p2; rep from * to end.
Row 4: K2, * yo, p2,  p2tog, p9, k2; rep from * to end.
Row 5: P2, * k8, k2tog, k1, yo, k2, p2; rep from * to end.
Row 6: K2, * p1, yo, p3,  p2tog, p7, k2; rep from * to end.
Row 7: P2, * k6, k2tog, k2, yo, k3, p2; rep from * to end.
Row 8: K2, * p2, yo, p4,  p2tog, p5, k2; rep from * to end.
Row 9: P2, * k4, k2tog, k3, yo, k4, p2; rep from * to end.
Row 10: K2, * p3, yo, p5,  p2tog, p3, k2; rep from * to end.
Row 11: P2, * k13, p2; rep from * to end.
Row 12: K2, * p13, k2; rep from * to end.
Row 13: P2, * k1, yo, ssk, k10, p2; rep from * to end.
Row 14: K2, * p9, ssp, p2, yo, k2; rep from * to end.
Row 15: P2, * k2, yo, k1, ssk, k8, p2; rep from * to end.
Row 16: K2, * p7, ssp, p3, yo, p1, k2; rep from * to end.
Row 17: P2, * k3, yo, k2, ssk, k6, p2; rep from * to end.
Row 18: K2, * p5, ssp, p4, yo, p2, k2; rep from * to end.
Row 19: P2, * k4, yo, k3, ssk, k4, p2; rep from * to end.
Row 20: K2, * p3, ssp, p5, yo, p3, k2; rep from * to end.

Knitting abbreviations:
K: Knit | P: Purl | Yo: Yarn over.
K2tog: Knit 2 sts together | Ssk: Slip slip knit.
Purl: Purl 2 sts together | Ssp: Slip slip purl.