A091675 Positive integers n such that the trajectory of n under the Reverse and Add! operation carried out in base 4 (presumably) does not join the trajectory of any m < n.

1, 3, 21, 22, 26, 29, 31, 55, 256, 258, 262, 266, 269, 271, 282, 286, 287, 302, 312, 413, 479, 511, 519, 551, 555, 719, 795, 799, 1026, 1029, 1034, 1037, 1066, 1549, 1790, 2863, 3087, 3119, 4096, 4098, 4102, 4104, 4106, 4108, 4109, 4113, 4114, 4116, 4117

Offset

1,2

Comments

The conjecture that the base-4 trajectories of the terms do not join is based on the observation that if the trajectories of two integers below 4120 join, this happens after at most 28 steps, while for any two terms listed above the trajectories do not join within 1000 steps. For pairs from 1, 3, 21, 22, 26, 29, 31, 55 this has even been checked for 5000 steps.

Base-4 analog of A070788.

Links

Table of n, a(n) for n=1..49.

Klaus Brockhaus, Illustration: Distribution of terms below 2000000

Index entries for sequences related to Reverse and Add!

Example

The trajectory of 2 is part of the trajectory of 1 (cf. A035524); the trajectory of 3 does not join the trajectory of 1 within 10000 steps; the trajectory of 21 does not join the trajectory of 1 or of 3 within 10000 steps.

Mathematica

limit = 10^3; utraj = {};
Select[Range[4120], (x = NestList[ # + IntegerReverse[#, 4] &, #, limit]; If[Intersection[x, utraj] == {}, utraj = Union[utraj, x]; True, utraj = Union[utraj, x]]) &] (* Robert Price, Oct 20 2019 *)

Crossrefs

Cf. A035524, A075421, A070788.

Sequence in context: A226319 A279842 A043081 * A067233 A007648 A273481

Adjacent sequences: A091672 A091673 A091674 * A091676 A091677 A091678

Keyword

base,nonn

Author

Klaus Brockhaus, Jan 28 2004

Status

approved