

A084531


Signature sequence of phi = (1+sqrt(5))/2 = 1.61803...


23



1, 2, 1, 3, 2, 4, 1, 3, 5, 2, 4, 1, 6, 3, 5, 2, 7, 4, 1, 6, 3, 8, 5, 2, 7, 4, 9, 1, 6, 3, 8, 5, 10, 2, 7, 4, 9, 1, 6, 11, 3, 8, 5, 10, 2, 7, 12, 4, 9, 1, 6, 11, 3, 8, 13, 5, 10, 2, 7, 12, 4, 9, 1, 14, 6, 11, 3, 8, 13, 5, 10, 2, 15, 7, 12, 4, 9, 1, 14, 6, 11, 3, 16, 8, 13, 5, 10, 2, 15, 7, 12, 4, 17, 9, 1
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OFFSET

1,2


COMMENTS

Arrange the numbers i+j*x (i,j >= 1) in increasing order; the sequence of i's is the signature of x; the sequence of j's is the signature of 1/x.
As a fractal sequence, if the first occurrence of each n is deleted, the remaining sequence is the original. That is, the upper trim of A084531 is A084531. Also, the lower trim of A084531 is A084531, meaning that if 1 is subtracted from every term and then all 0s are deleted, the result is the original sequence. Every fractal sequence begets an interspersion; the interspersion of A084531 is A167267.  Clark Kimberling, Oct 31 2009


REFERENCES

Clark Kimberling, "Fractal Sequences and Interspersions," Ars Combinatoria 45 (1997) 157168.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
Glen Joyce C. Dulatre, Jamilah V. Alarcon, Vhenedict M. Florida, Daisy Ann A. Disu, On Fractal Sequences, DMMMSUCAS Science Monitor (20162017) Vol. 15 No. 2, 109113.
Casey Mongoven, Sonification of multiple Fibonaccirelated sequences, Annales Mathematicae et Informaticae, 41 (2013) pp. 175192.


MATHEMATICA

x = GoldenRatio; Take[Transpose[Sort[Flatten[Table[{i + j*x, i}, {i, 30}, {j, 20}], 1], #1[[1]] < #2[[1]] &]][[2]], 100] (* Clark Kimberling, Nov 10 2012 *)


CROSSREFS

Cf. A084532, A167267.
Sequence in context: A087470 A191475 A158456 * A023129 A007337 A167430
Adjacent sequences: A084528 A084529 A084530 * A084532 A084533 A084534


KEYWORD

nonn


AUTHOR

Henry Bottomley, May 28 2003


STATUS

approved



