A070788 Positive integers n such that the Reverse and Add! trajectory of n (presumably) does not join the trajectory of any m < n.

1, 3, 5, 7, 9, 100, 102, 106, 108, 111, 112, 113, 114, 116, 117, 118, 119, 122, 124, 128, 133, 135, 137, 138, 166, 184, 186, 196, 199, 359, 399, 459, 539, 659, 679, 739, 759, 779, 799, 859, 879, 919, 939, 959, 979, 999, 1000, 1006, 1011, 1013, 1022, 1033, 1037

Offset: 1

Author

Klaus Brockhaus, May 07 2002, revised Oct 15 2003

Keywords

• base
• nonn

Comments

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.

Examples

			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.
		

Links

• Klaus Brockhaus, Illustration: Distribution of terms below 2000000
• Klaus Brockhaus, List of terms below 2000000
• Index entries for sequences related to Reverse and Add!

Crossrefs

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

Programs

Mathematica

limit = 10^3; utraj = {};
Select[Range[1037], (x = NestList[ # + IntegerReverse[#] &, #, limit]; If[Intersection[x, utraj] == {}, utraj = Union[utraj, x]; True, utraj = Union[utraj, x]]) &] (* Robert Price, Oct 20 2019 *)