[go: up one dir, main page]

login
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
OFFSET
1,2
COMMENTS
As a fractal sequence, A163256 contains every positive integer; indeed, A163256 properly contains itself (infinitely many times).
LINKS
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 24 2009
STATUS
approved