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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 (list; graph; refs; listen; history; text; internal format)
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.

This is subsequence of A003603. - Clark Kimberling, Oct 26 2021

a(n) is the number of the row of the Wythoff array (A035513) that contains the n-th Wythoff pair; e.g., the 6th Wythoff pair is ([6*r]),([6*r^2)], which is in row 4 of the Wythoff array.  (Here, [ ] = floor, and r = golden ratio = (1 + sqrt(5))/2.) - Clark Kimberling, Oct 26 2021

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) 153-158.

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. A003603, A035513, 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

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Last modified July 1 02:58 EDT 2022. Contains 354947 sequences. (Running on oeis4.)