Search: id:A063048
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%I A063048
%S A063048 196,879,1997,7059,10553,10563,10577,10583,10585,10638,10663,10668,
%T A063048 10697,10715,10728,10735,10746,10748,10783,10785,10787,10788,10877,
%U A063048 10883,10963,10965,10969,10977,10983,10985,12797,12898,13097,13197
%N A063048 Numbers n such that the Reverse and Add! trajectory of n (presumably) 
               does not reach a palindrome and does not join the trajectory of any 
               term m < n.
%C A063048 The starting number n is regarded as part of the trajectory, so palindromes 
               are excluded from the sequence. A088753 is obtained if palindromes 
               are not excluded. The smallest term in A063048 but not in A088753 
               is 19098, the smallest term in A088753 but not in A063048 is 9999.
%C A063048 Subsequence of A023108. Sequence A070788 is similarly defined, but palindromes 
               are irrelevant. Corresponding sequences for other bases are A075252 
               (base 2), A077405 (base 3), A075421 (base 4).
%C A063048 If the trajectory of a number k joins the trajectory of a smaller number 
               which is a term of the present sequence, then this occurs after very 
               few Reverse and Add! steps (at most 8 for k < 100000, at most 10 
               for k < 1000000). On the other hand, the trajectories of the terms 
               < 14000 do not join the trajectory of any smaller term within at 
               least 1500 steps. This is the precise meaning of "presumably" in 
               the definition.
%C A063048 The terms are rather unevenly distributed. They form clusters, especially 
               above 10^4, 10^5, 10^6, ... . The interval from 10000 to 11000 for 
               example contains 26 terms, whereas only two terms occur in the interval 
               from 90000 to 100000.
%H A063048 Klaus Brockhaus, <a href="a063048.gif">Illustration: Distribution of 
               terms below 2000000</a>
%H A063048 Klaus Brockhaus, <a href="a063048.txt">List of terms below 2000000</a>
%H A063048 <a href="Sindx_Res.html#RAA">Index entries for sequences related to Reverse 
               and Add!</a>
%e A063048 1997 is a term since the trajectory of 1997 (presumably) does not lead 
               to a number which occurs in the trajectory of 196 or of 879 (actually 
               checked for the first 10000 terms of these trajectories). The trajectory 
               of 1997 joins the
%e A063048 trajectory of 106 at 97768 (cf. A070796), but 106 is not a term of the 
               present sequence.
%Y A063048 Cf. A033865, A023108, A006960, A063049 - A063065, A088753, A070788, A075252, 
               A077405, A075421, A070796.
%Y A063048 Sequence in context: A092231 A089493 A088753 this_sequence A006960 A014798 
               A061622
%Y A063048 Adjacent sequences: A063045 A063046 A063047 this_sequence A063049 A063050 
               A063051
%K A063048 base,nonn
%O A063048 1,1
%A A063048 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 07 2001, revised 
               Nov 04 2003

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