OFFSET
1,2
COMMENTS
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.
EXAMPLE
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.
MATHEMATICA
limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
utraj = NestList[# + IntegerReverse[#, 2] &, 1, limit];
Flatten@{1, Select[Range[2, 4189], (l = Length@NestWhileList[# + IntegerReverse[#, 2] &, #, ! MemberQ[utraj, #] &, 1, limit];
utraj = Union[utraj, NestList[# + IntegerReverse[#, 2] &, #, limit]];
l == limit + 1) &]} (* Robert Price, Nov 03 2019 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Klaus Brockhaus, Feb 25 2004
STATUS
approved