%I
%S 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,
%T 21,22,7,23,24,8,25,26,27,28,9,29,30,10,31,32,3,33,34,11,35,36,12,37,
%U 38,4,39,40,13,41,42,14,43,44,1,45,46,15,47,48,16,49,50,5,51,52,17,53,54,18
%N Representation of a dense parasequence.
%C (1) A fractal sequence. (2) The parasequence may be regarded as a sort of "limit" of the concatenated segments. The parasequence (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 parasequence 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 C. Kimberling, Proper selfcontaining sequences, fractal sequences and parasequences, preprint, 2007.
%H Clark Kimberling, <a href="/A133108/b133108.txt">Table of n, a(n) for n = 1..10000</a>
%H Clark Kimberling, <a href="/A131987/a131987.pdf">Proper selfcontaining sequences, fractal sequences and parasequences</a>, unpublished manuscript, 2007, cached copy, with permission.
%e The first segment is 1,2; the 2nd is 3,4,1,5,6,2,7,8; the 4th begins with 27,28,9 and ends with 26,79,80.
%t Flatten@NestList[Riffle[Range[Length[#] + 1, 3 Length[#] + 2], #, 3] &, {1, 2}, 3] (* _Birkas Gyorgy_, Mar 11 2011 *)
%Y Cf. A131987.
%K nonn
%O 1,2
%A _Clark Kimberling_, Sep 12 2007
