

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.


2



1021, 3623, 4327, 4382, 4404, 4413, 4444, 4500, 4502, 4518, 4522, 4528, 4530, 4575, 4592, 4594, 5117, 5502, 5629, 6270, 7806, 8247, 8607, 12503, 12527, 12535, 16319, 16383, 16815, 20711, 20975, 24751, 25015, 28351, 28415, 28671, 28775, 28791, 33757, 33766, 34254, 34286, 34757, 34781, 35268, 35276
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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 recordsetting 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.
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 contextfree grammar with alphabet = {0,1,2,3,4,5,6,7} and production rules:
S > S_a  S_b  S_c  S_d  S_e  S_f  S_g  S_h,
S_a > 10 T_a 00, T_a > 7 T_a 0  777670,
S_b > 11 T_b 01, T_b > 0 T_b 7  076667,
S_c > 22 T_c 12, T_c > 0 T_c 7  065557,
S_d > 44 T_d 34, T_d > 0 T_d 7  043337,
S_e > 10 T_e 000, T_e > 7 T_e 0  777670,
S_f > 11 T_f 701, T_f > 0 T_f 7  007567,
S_g > 22 T_g 712, T_g > 0 T_g 7  006357,
S_h > 44 T_h 734, T_h > 0 T_h 7  003737;
i.e., the cycle length is 8.
For all other terms up to and including a(649) = 527823, no such structure has been obtained.


LINKS

Table of n, a(n) for n=1..46.


CROSSREFS

Cf. A306600, A306599, A306851, A306850.
Base8 analog of A075252 (base 2), A077405 (base 3), A075421 (base 4) and A063048 (base 10).
Sequence in context: A082059 A081633 A020388 * A287639 A261676 A165097
Adjacent sequences: A306593 A306594 A306595 * A306597 A306598 A306599


KEYWORD

nonn,base


AUTHOR

A.H.M. Smeets, Feb 27 2019


STATUS

approved



