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Let 3 ≤ d1 ≤ d2 ≤ d3 be integers. We show the following results: (1) If d2 is a prime number and d1 gcd(d1;d3) ≠ 2, then (d1; d2; d3) is a multidegree of a tame automorphism if and only if d1 = d2 or d3 ε d1N + d2N; (2) If d3 is a prime number and gcd(d1; d2) = 1, then (d1; d2; d3) is a multidegree of a tame automorphism if and only if d3 ε d1N+d2N. We also show that the condition d1 gcd(d1;d3) ≠ 2 in (1) cannot be removed.

Multidegrees of tame automorphisms with one prime number