A077405 Trajectory of n under the Reverse and Add! operation carried out in base 3 (presumably) does not reach a palindrome and (presumably) does not join the trajectory of any term m < n.

103, 746, 805, 2231, 2326, 2671, 2725, 2959, 2969, 3679, 4421, 4430, 4439, 4448, 5894, 6626, 6638, 6686, 6698, 6733, 6741, 6779, 6789, 6793, 6943, 7124, 7365, 7849, 8093, 8801, 8836, 10771, 11078, 11158, 13184, 13361, 17558, 17639, 19115, 19196, 19733, 19895, 19901, 19907, 20106, 20124, 20149, 20161

Offset: 1

Author

Klaus Brockhaus, Nov 05 2002

Keywords

• base
• nonn

Comments

Base 3 analog of A075252 (base 2), A075421 (base 4) and A063048 (base 10); subsequence of A077404. - A proof that the base 3 trajectory does not contain a palindrome has been found up to now for none of the terms. - If the trajectory of an integer k joins the trajectory of a smaller integer which is a term of the present sequence, then this occurs after very few Reverse and Add! steps (at most 9 for k < 20000). On the other hand, the trajectories of the terms of this sequence do not join the trajectory of any smaller term within at least 1000 steps.

Examples

			805 is a term since the trajectory of 805 (presumably) does not lead to a number which occurs in the trajectory of 103 or of 746.
		

Links

• A.H.M. Smeets, Table of n, a(n) for n = 1..529
• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A063048, A075252, A075421, A077404.

Programs

Mathematica

limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
utraj = {};
Select[Range[0,21000], (i = 0;
   x = NestWhileList[(i++; # + IntegerReverse[#, 3]) &, #, # !=
        IntegerReverse[#, 3] && i < limit  &];
   If[i >= limit  && Intersection[x, utraj] == {},
    utraj = Union[utraj, x]; True,
    utraj = Union[utraj, x]]) &]
(* Robert Price, Oct 19 2019 *)

Extensions

Offset changed to 1 by A.H.M. Smeets, Feb 14 2019

a(41)-a(48) from A.H.M. Smeets, Feb 18 2019