On Collatz Words, Sequences, and Trees
Motivated by recent work of Trümper, we consider the general Collatz
word (up-down pattern) and the sequences following this pattern. We
derive recurrences for the first and last sequence entries from
repeated application of the general solution of a binary linear
inhomogeneous Diophantine equation. We solve these recurrences and
also discuss the Collatz tree.
Full version: pdf,
(Concerned with sequences
Received April 10 2014;
revised versions received October 2 2014; November 5 2014; November 11 2014.
Published in Journal of Integer Sequences, December 12 2014.
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