%I A133108
%S A133108 1,2,3,4,1,5,6,2,7,8,9,10,3,11,12,4,13,14,1,15,16,5,17,18,6,19,20,2,21,
%T A133108 22,7,23,24,8,25,26,27,28,9,29,30,10,31,32,3,33,34,11,35,36,12,37,38,4,
%U A133108 39,40,13,41,42,14,43,44,1,45,46,15,47,48,16,49,50,5,51,52,17,53,54,18
%N A133108 Representation of a dense para-sequence.
%C A133108 (1) A fractal sequence. (2) The para-sequence may be regarded as a sort 
               of "limit" of the concatenated segments. The para-sequence (itself 
               not a sequence) is dense in the sense that every pair of terms i 
               and j are separated by another term (and hence separated by infinitely 
               many terms. (3) The para-sequence accounts for positions of triadic 
               rational numbers in the following way: 1/3 < 2/3 matches the segment 
               1,2; 1/9 < 2/9 < 1/3 < 4/9 < 5/9 < 2/3 < 7/9 < 8/9 matches the segment 
               3,4,1,5,6,2,7,8, etc.
%D A133108 C. Kimberling, Proper self-containing sequences, fractal sequences and 
               para-sequences, preprint, 2007.
%F A133108 Start with initial segment 1,2 and isolate them using 3-to-8 like this: 
               3,4,1,5,6,2,7,8. (This is the 2nd segment.) Then isolate those using 
               9-to-26, like this: 9,10,3,11,12,4,13,14,1,...8,25,26. (This is the 
               3rd segment.) Continue and concatenate.
%e A133108 The first segment is 1,2; the 2nd is 3,4,1,5,6,2,7,8; the
%e A133108 4th begins with 27,28,9 and ends with 26,79,80.
%Y A133108 Cf. A131987.
%Y A133108 Sequence in context: A115994 A071437 A129709 this_sequence A055441 A104717 
               A067003
%Y A133108 Adjacent sequences: A133105 A133106 A133107 this_sequence A133109 A133110 
               A133111
%K A133108 nonn
%O A133108 1,2
%A A133108 Clark Kimberling (ck6(AT)evansville.edu), Sep 12 2007