cp's OEIS Frontend

A306596 Trajectory of n under the Reverse and Add! operation carried out in base 8 (presumably) does not reach a palindrome and (presumably) does not join the trajectory of any term m < n.

%I A306596 #30 Jan 11 2020 17:57:08
%S A306596 1021,3623,4327,4382,4404,4413,4444,4500,4502,4518,4522,4528,4530,
%T A306596 4575,4592,4594,5117,5502,5629,6270,7806,8247,8607,12503,12527,12535,
%U A306596 16319,16383,16815,20711,20975,24751,25015,28351,28415,28671,28775,28791,33757,33766,34254,34286,34757,34781,35268,35276
%N A306596 Trajectory of n under the Reverse and Add! operation carried out in base 8 (presumably) does not reach a palindrome and (presumably) does not join the trajectory of any term m < n.
%C A306596 A number is considered here (presumably) a Lychrel number in base 8 if it does not reach a palindrome within 100 steps more than the actual record. For those record numbers of steps, see A306600; for the corresponding record-setting numbers, see A306599. Futhermore, a Lychrel number is considered not to reach the trajectory of any smaller Lychrel number if it does not reach a trajectory of a smaller Lychrel number within 100 steps more than the actual record. For those record number of steps see A306851, and its corresponding record setting numbers, see A306850.
%C A306596 For a(11) = 4522 we obtain a cyclic structure of the terms in its trajectory (starting at the 12th term in the trajectory) which can be represented by the context-free grammar with alphabet = {0,1,2,3,4,5,6,7} and production rules:
%C A306596   S -> S_a | S_b | S_c | S_d | S_e | S_f | S_g | S_h,
%C A306596   S_a -> 10 T_a  00, T_a -> 7 T_a 0 | 777670,
%C A306596   S_b -> 11 T_b  01, T_b -> 0 T_b 7 | 076667,
%C A306596   S_c -> 22 T_c  12, T_c -> 0 T_c 7 | 065557,
%C A306596   S_d -> 44 T_d  34, T_d -> 0 T_d 7 | 043337,
%C A306596   S_e -> 10 T_e 000, T_e -> 7 T_e 0 | 777670,
%C A306596   S_f -> 11 T_f 701, T_f -> 0 T_f 7 | 007567,
%C A306596   S_g -> 22 T_g 712, T_g -> 0 T_g 7 | 006357,
%C A306596   S_h -> 44 T_h 734, T_h -> 0 T_h 7 | 003737;
%C A306596 i.e., the cycle length is 8.
%C A306596 For all other terms up to and including a(649) = 527823, no such structure has been obtained.
%Y A306596 Cf. A306600, A306599, A306851, A306850.
%Y A306596 Base-8 analog of A075252 (base 2), A077405 (base 3), A075421 (base 4) and A063048 (base 10).
%K A306596 nonn,base
%O A306596 1,1
%A A306596 _A.H.M. Smeets_, Feb 27 2019