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We calculate the alternating number of torus knots with braid index 4 andless. For the lower bound, we use the upsilon-invariant recently introduced byOzsv\'ath, Stipsicz, and Szab\'o. For the upper bound, we use a known bound forbraid index $3$ and a new bound for braid index $4$. Both bounds coincide, sothat we obtain a sharp result.

Alternating numbers of torus knots with small braid index