%I A070788
%S A070788 1,3,5,7,9,100,102,106,108,111,112,113,114,116,117,118,119,122,124,128,
%T A070788 133,135,137,138,166,184,186,196,199,359,399,459,539,659,679,739,759,
%U A070788 779,799,859,879,919,939,959,979,999,1000,1006,1011,1013,1022,1033,1037
%N A070788 Positive integers n such that the Reverse and Add! trajectory of n (presumably) 
               does not join the trajectory of any m < n.
%C A070788 The conjecture that the trajectories of the terms of this sequence do 
               not join is based on the observation that if the trajectories of 
               two integers below 10000 join, this happens after at most 15 steps, 
               while for any two terms the trajectories do not join within 1200 
               steps. For pairs from 1, 3, 5, 7, 9, 100, 102, 106 this has even 
               been checked for 10000 steps.
%C A070788 The positive integers are the domain of the equivalence relation 'the 
               trajectories of a and b join'; each of its presumably infinitely 
               many equivalence classes is represented by a term of this sequence. 
               Each class contains infinitely many integers (cf. A070789 - A070798). 
               In such a class the relation 'the trajectory of a is part of the 
               trajectory of b' is a partial order for which a term c is a maximal 
               element if it is in A067031 (integers not of the form k + reverse(k) 
               for any k) and the integer at which the trajectories of a and b join 
               is the greatest lower bound of a and b.
%H A070788 Klaus Brockhaus, <a href="a070788.gif">Illustration: Distribution of 
               terms below 2000000</a>
%H A070788 Klaus Brockhaus, <a href="a070788.txt">List of terms below 2000000</a>
%H A070788 <a href="Sindx_Res.html#RAA">Index entries for sequences related to Reverse 
               and Add!</a>
%e A070788 The trajectory of 2 is part of the trajectory of 1; the trajectory of 
               3 does not join the trajectory of 1 within 10000 steps; the trajectory 
               of 5 does not join the trajectory of 1 or of 3 within 10000 steps.
%Y A070788 Cf. A006960, A063048, A067031, A070789 - A070798, A063049.
%Y A070788 Sequence in context: A092046 A085951 A132286 this_sequence A030148 A068061 
               A062887
%Y A070788 Adjacent sequences: A070785 A070786 A070787 this_sequence A070789 A070790 
               A070791
%K A070788 base,nonn
%O A070788 1,2
%A A070788 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 07 2002, revised 
               Oct 15 2003