

A120873


Fractal sequence of the Wythoff difference array (A080164).


0



1, 1, 2, 3, 1, 4, 2, 5, 6, 3, 7, 8, 1, 9, 4, 10, 11, 2, 12, 5, 13, 14, 6, 15, 16, 3, 17, 7, 18, 19, 8, 20, 21, 1, 22, 9, 23, 24, 4, 25, 10, 26, 27, 11, 28, 29, 2, 30, 12, 31, 32, 5, 33, 13, 34, 35, 14, 36, 37, 6, 38, 15, 39, 40, 16, 41, 42, 3, 43, 17, 44, 45, 7, 46, 18, 47, 48, 19, 49
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OFFSET

1,3


COMMENTS

A fractal sequence f contains itself as a proper subsequence; e.g., if you delete the first occurrence of each positive integer, the remaining sequence is f; thus f properly contains itself infinitely many times.


REFERENCES

Clark Kimberling, The Wythoff difference array, in Applications of Fibonacci Numbers, vol.10, Proceedings of the Eleventh International Conference on Fibonacci Numbers and Their Applications, William Webb, editor, Congressus Numerantium, Winnipeg, Manitoba 194 (2009) 153158.


LINKS

Table of n, a(n) for n=1..79.
N. J. A. Sloane, Classic Sequences.


EXAMPLE

The fractal sequence f(n) of a dispersion D={d(g,h,)} is defined as follows.
For each positive integer n there is a unique (g,h) such that n=d(g,h) and
f(n)=g.
So f(7)=2 because the row of the WDA in which 7 occurs is row 2.


CROSSREFS

Cf. A080164.
Sequence in context: A265579 A336879 A340313 * A125161 A331791 A125933
Adjacent sequences: A120870 A120871 A120872 * A120874 A120875 A120876


KEYWORD

nonn


AUTHOR

Clark Kimberling, Jul 10 2006


STATUS

approved



