A091675 - OEIS

%I #11 Oct 20 2019 22:03:53

%S 1,3,21,22,26,29,31,55,256,258,262,266,269,271,282,286,287,302,312,

%T 413,479,511,519,551,555,719,795,799,1026,1029,1034,1037,1066,1549,

%U 1790,2863,3087,3119,4096,4098,4102,4104,4106,4108,4109,4113,4114,4116,4117

%N 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.

%C 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.

%C Base-4 analog of A070788.

%H Klaus Brockhaus, <a href="/A091675/a091675.gif">Illustration: Distribution of terms below 2000000</a>

%H <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>

%e 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.

%t limit = 10^3; utraj = {};

%t 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 *)

%Y Cf. A035524, A075421, A070788.

%K base,nonn

%O 1,2

%A _Klaus Brockhaus_, Jan 28 2004