A092210 - OEIS

%I #13 Nov 03 2019 22:41:57

%S 1,16,64,74,98,107,259,266,271,275,298,398,442,454,522,794,911,1027,

%T 1046,1057,1066,1070,1073,1076,1081,1082,1085,1115,1274,1422,1562,

%U 1570,1967,2070,2329,3106,3355,3871,4099,4114,4120,4126,4136,4152,4182,4189

%N 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 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 Base-2 analog of A070788 (base 10) and A091675 (base 4).

%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. 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 limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)

%t utraj = NestList[# + IntegerReverse[#, 2] &, 1, limit];

%t Flatten@{1, Select[Range[2, 4189],   (l = Length@NestWhileList[# + IntegerReverse[#, 2] &, #, ! MemberQ[utraj, #] &, 1, limit];

%t   utraj = Union[utraj, NestList[# + IntegerReverse[#, 2] &, #, limit]];

%t   l == limit + 1) &]} (* _Robert Price_, Nov 03 2019 *)

%Y Cf. A035522, A075252, A070788, A091675.

%K nonn,base

%O 1,2

%A _Klaus Brockhaus_, Feb 25 2004