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Fractal sequence of the interspersion A163257.
5

%I #9 Jan 05 2025 19:51:39

%S 1,2,3,4,1,2,5,3,6,4,1,2,7,5,3,8,6,4,1,2,9,7,5,3,10,8,6,4,1,2,11,9,7,

%T 5,3,12,10,8,6,4,1,2,13,11,9,7,5,3,14,12,10,8,6,4,1,2,15,13,11,9,7,5,

%U 3,16,14,12,10,8,6,4,1,2,17,15,13,11,9,7,5,3,18,16,14,12,10,8,6,4

%N Fractal sequence of the interspersion A163257.

%C As a fractal sequence, A163258 contains every positive integer; indeed, A163258 properly contains itself (infinitely many times).

%H Clark Kimberling, <a href="https://web.archive.org/web/2024*/https://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 4

%e 1 2 5 3 6 4

%e 1 2 7 5 3 8 6 4

%e 1 2 9 7 5 3 10 8 6 4

%e For n>1, the n-th segment arises from the (n-1)st by inserting 2*n+1 at position 3 and 2*n+2 at position n+3.

%Y Cf. A163253, A163254, A163255, A163256, A163258.

%K nonn

%O 1,2

%A _Clark Kimberling_, Jul 24 2009