A163258 Fractal sequence of the interspersion A163257.

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, 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, 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

Offset: 1

Author

Clark Kimberling, Jul 24 2009

Keywords

• nonn

Comments

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

Examples

			Append the following segments:
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
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.
		

Links

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

Crossrefs

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