Knot adjacency and satellites

A knot K is called n-adjacent to the unknot, if K admits a projection containing n generalized crossings such that changing any 0<m⩽n of them yields a projection of the unknot. We show that a non-trivial satellite knot K is n-adjacent to the unknot, for some n>0, if and only if it is n-adjacent to the unknot in any companion solid torus. In particular, every model knot of K is n-adjacent to the unknot. Along the way of proving these results, we also show that 2-bridge knots of the form Kp/q, where p/q=[2q1,2q2] for some q1,q2∈Z, are precisely those knots that have genus one and are 2-adjacent to the unknot.