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

Author

Clark Kimberling, Jul 24 2009

Keywords

• nonn

Comments

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

Examples

			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.
		

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.

Crossrefs

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

Programs

Mathematica

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