A163256 Fractal sequence of the interspersion A163253.

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

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 A341826 A257669

Adjacent sequences: A163253 A163254 A163255 * A163257 A163258 A163259

Keyword

nonn

Author

Clark Kimberling, Jul 24 2009

Status

approved