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A163256 Fractal sequence of the interspersion A163253. 5
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

As a fractal sequence, A163256 contains every positive integer; indeed, A163256 properly contains itself (infinitely many times).

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..2500

Clark Kimberling, Doubly interspersed sequences, double interspersions and fractal sequences, The Fibonacci Quarterly 48 (2010) 13-20.

EXAMPLE

Append the following segments:

1 2 3

1 2 4 3 5

1 2 4 6 3 5 7

1 2 4 6 8 3 5 7 9

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.

MATHEMATICA

Flatten[FoldList[Append[Insert[#1, 2 #2, #2 + 1], 2 #2 + 1] &, {1}, Range[10]]] (* Birkas Gyorgy, Jul 09 2012 *)

CROSSREFS

Cf. A163253, A163254, A163255, A163257, A163258.

Sequence in context: A029271 A035459 A048232 * A199263 A257669 A181803

Adjacent sequences:  A163253 A163254 A163255 * A163257 A163258 A163259

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 24 2009

STATUS

approved

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Last modified July 27 04:53 EDT 2017. Contains 289841 sequences.