cp's OEIS Frontend

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.

%I A077405 #23 Oct 19 2019 12:37:23
%S A077405 103,746,805,2231,2326,2671,2725,2959,2969,3679,4421,4430,4439,4448,
%T A077405 5894,6626,6638,6686,6698,6733,6741,6779,6789,6793,6943,7124,7365,
%U A077405 7849,8093,8801,8836,10771,11078,11158,13184,13361,17558,17639,19115,19196,19733,19895,19901,19907,20106,20124,20149,20161
%N 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.
%C A077405 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.
%H A077405 A.H.M. Smeets, <a href="/A077405/b077405.txt">Table of n, a(n) for n = 1..529</a>
%H A077405 <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%e A077405 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.
%t A077405 limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
%t A077405 utraj = {};
%t A077405 Select[Range[0,21000], (i = 0;
%t A077405    x = NestWhileList[(i++; # + IntegerReverse[#, 3]) &, #, # !=
%t A077405         IntegerReverse[#, 3] && i < limit  &];
%t A077405    If[i >= limit  && Intersection[x, utraj] == {},
%t A077405     utraj = Union[utraj, x]; True,
%t A077405     utraj = Union[utraj, x]]) &]
%t A077405 (* _Robert Price_, Oct 19 2019 *)
%Y A077405 Cf. A063048, A075252, A075421, A077404.
%K A077405 base,nonn
%O A077405 1,1
%A A077405 _Klaus Brockhaus_, Nov 05 2002
%E A077405 Offset changed to 1 by _A.H.M. Smeets_, Feb 14 2019
%E A077405 a(41)-a(48) from _A.H.M. Smeets_, Feb 18 2019