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%I #15 Dec 12 2016 01:51:34
%S 1,2,3,1,2,4,3,5,1,2,4,6,3,5,7,1,2,4,6,8,3,5,7,9,1,2,4,6,8,10,3,5,7,9,
%T 11,1,2,4,6,8,10,12,3,5,7,9,11,13,1,2,4,6,8,10,12,14,3,5,7,9,11,13,15,
%U 1,2,4,6,8,10,12,14,16,3,5,7,9,11,13,15,17,1,2,4,6,8,10,12,14,16,18,3,5,7
%N Fractal sequence of the interspersion A163253.
%C As a fractal sequence, A163256 contains every positive integer; indeed, A163256 properly contains itself (infinitely many times).
%H G. C. Greubel, <a href="/A163256/b163256.txt">Table of n, a(n) for n = 1..2500</a>
%H Clark Kimberling, <a href="http://www.fq.math.ca/Papers1/48-1/Kimberling.pdf">Doubly interspersed sequences, double interspersions and fractal sequences</a>, The Fibonacci Quarterly 48 (2010) 13-20.
%e Append the following segments:
%e 1 2 3
%e 1 2 4 3 5
%e 1 2 4 6 3 5 7
%e 1 2 4 6 8 3 5 7 9
%e For n>1, the n-th segment arises from the (n-1)st by inserting 2*n at position n+1 and appending 2*n+1 at position 2*n+1.
%t Flatten[FoldList[Append[Insert[#1, 2 #2, #2 + 1], 2 #2 + 1] &, {1}, Range[10]]] (* _Birkas Gyorgy_, Jul 09 2012 *)
%Y Cf. A163253, A163254, A163255, A163257, A163258.
%K nonn
%O 1,2
%A _Clark Kimberling_, Jul 24 2009
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