cp's OEIS Frontend

A092210 Positive integers n such that the trajectory of n under the Reverse and Add! operation carried out in base 2 (presumably) does not join the trajectory of any m < n.

%I A092210 #13 Nov 03 2019 22:41:57
%S A092210 1,16,64,74,98,107,259,266,271,275,298,398,442,454,522,794,911,1027,
%T A092210 1046,1057,1066,1070,1073,1076,1081,1082,1085,1115,1274,1422,1562,
%U A092210 1570,1967,2070,2329,3106,3355,3871,4099,4114,4120,4126,4136,4152,4182,4189
%N A092210 Positive integers n such that the trajectory of n under the Reverse and Add! operation carried out in base 2 (presumably) does not join the trajectory of any m < n.
%C A092210 The conjecture that the base 2 trajectories of the terms do not join is based on the observation that if the trajectories of two integers < 12000 join, this happens after at most 93 steps, while for any two terms listed above the trajectories do not join within 1000 steps. For pairs from 1, 16, 64, 74, 98, 107 this has even been checked for 5000 steps.
%C A092210 Base-2 analog of A070788 (base 10) and A091675 (base 4).
%H A092210 <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%e A092210 The trajectory of 2 is part of the trajectory of 1 (cf. A035522); the trajectory of 16 does not join the trajectory of 1 within 10000 steps; the trajectory of 64 does not join the trajectory of 1 or of 16 within 10000 steps.
%t A092210 limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
%t A092210 utraj = NestList[# + IntegerReverse[#, 2] &, 1, limit];
%t A092210 Flatten@{1, Select[Range[2, 4189],   (l = Length@NestWhileList[# + IntegerReverse[#, 2] &, #, ! MemberQ[utraj, #] &, 1, limit];
%t A092210   utraj = Union[utraj, NestList[# + IntegerReverse[#, 2] &, #, limit]];
%t A092210   l == limit + 1) &]} (* _Robert Price_, Nov 03 2019 *)
%Y A092210 Cf. A035522, A075252, A070788, A091675.
%K A092210 nonn,base
%O A092210 1,2
%A A092210 _Klaus Brockhaus_, Feb 25 2004