2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57591Recently it has been found that some special subsequences within a Farey sequence play a crucial role in determining the ranges of coupling constant for which quantum soliton states can exist for an integrable derivative nonlinear Schrodinger model. In this article, we find a novel mapping which connects two such subsequences belonging to Farey sequences of different orders. By using this mapping, we construct an algorithm to generate all of these special subsequences within a Farey sequence. We also derive the continued fraction expansions for all the elements belonging to a subsequence and observe a close connection amongst the corresponding expansion coefficients.latex, 8 pagesMathematical PhysicsHigh Energy Physics - TheoryNumber TheoryExactly Solvable and Integrable Systemstext