For every p at least 2 there exist knots with arbitrarily large gaps between tu_{p-1} and tu_p, and torus knots with unbounded gaps between tu_1 and tu_2.
Bordered H eegaard F loer homology and the tau-invariant of cable knots
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Gaps between consecutive untwisting numbers
For every p at least 2 there exist knots with arbitrarily large gaps between tu_{p-1} and tu_p, and torus knots with unbounded gaps between tu_1 and tu_2.