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In the paper, from the point of view of recurrent numbers of the Jacobsthaltype, the Collatz problem with the general aq+-1 function of conjecture oddpositive integers q from the set of natural numbers is investigated. Formulatedbranching rules from nodes with generalized Jacobsthal numbers of the so-calledJacobsthal tree. It is shown that Collatz trajectories are formed in thereverse direction of the Jacobsthal tree. It is shown that unlike the classicalCollatz problem, in which the Collatz sequence for a finite number ofiterations leads to the unit element, for functions with factors 3 and 5, theCollatz sequence for a finite number of iterations does not reach the unitelement. An analytical model is proposed that relates the iteration number ofdoubling (or halving the number in the reverse direction) number between twoodd-numbered branch nodes. It is shown that for an arbitrary number, Collatzand Jacobsthal trajectories develop in the respective directions, and theJacobsthal trajectory for a finite number of iterations leads to an elementthat is a multiple of the factor a in the function aq+-1.

The Collatz problem (a*q+-1,a=1,3,5,...) from the point of view of transformations of Jacobsthal numbers