A tame cycle of period 15 in a subprime Tribonacci sequence

Barrows, Noye, Uttormark and Wright asked whether a subprime Tribonacci sequence can have a tame cycle of length greater than 4. We give an explicit cycle of least period 15 whose terms have greatest common divisor 919. The verification uses fifteen multiplication identities, elementary divisibility checks, and two primality tests on six-digit numbers. Scaling its primitive representative by any integer whose least prime factor is at least 919 gives infinitely many tame cycles of the same period. For the prescribed signature, the closure condition is a bilinear equation with the unique integer solution (919, 307). Two diagonal cofactors of the cycle matrix relate its factorisation to coordinates of the primitive cycle. Six pages; LaTeX source included. The three verification programs are archived separately and are cited in the text. MSC 2020: 11B37, 11Y11.