1,2

The conjecture that the trajectories of the terms of this sequence do not join is based on the observation that if the trajectories of two integers below 10000 join, this happens after at most 15 steps, while for any two terms the trajectories do not join within 1200 steps. For pairs from 1, 3, 5, 7, 9, 100, 102, 106 this has even been checked for 10000 steps.

The positive integers are the domain of the equivalence relation 'the trajectories of a and b join'; each of its presumably infinitely many equivalence classes is represented by a term of this sequence. Each class contains infinitely many integers (cf. A070789 - A070798). In such a class the relation 'the trajectory of a is part of the trajectory of b' is a partial order for which a term c is a maximal element if it is in A067031 (integers not of the form k + reverse(k) for any k) and the integer at which the trajectories of a and b join is the greatest lower bound of a and b.

Klaus Brockhaus, Illustration: Distribution of terms below 2000000

Klaus Brockhaus, List of terms below 2000000

Index entries for sequences related to Reverse and Add!

The trajectory of 2 is part of the trajectory of 1; the trajectory of 3 does not join the trajectory of 1 within 10000 steps; the trajectory of 5 does not join the trajectory of 1 or of 3 within 10000 steps.

Cf. A006960, A063048, A067031, A070789 - A070798, A063049.

Sequence in context: A092046 A085951 A132286 this_sequence A030148 A068061 A062887

Adjacent sequences: A070785 A070786 A070787 this_sequence A070789 A070790 A070791

base,nonn

Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 07 2002, revised Oct 15 2003