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 0's 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
The positions of the first occurrence of i in this sequence, i>=1, form sequence A255977. That is, 1 occurs for the first time at position 1, 2 at position 2, 3 at position 4, 4 at position 6, and 1,2,4,6, ... is A255977. - Jeffrey Shallit, Jun 28 2024
REFERENCES
Clark Kimberling, "Fractal Sequences and Interspersions," Ars Combinatoria 45 (1997) 157-168.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Glen Joyce C. Dulatre, Jamilah V. Alarcon, Vhenedict M. Florida, and Daisy Ann A. Disu, On Fractal Sequences, DMMMSU-CAS Science Monitor (2016-2017) Vol. 15 No. 2, 109-113.
Casey Mongoven, Sonification of multiple Fibonacci-related sequences, Annales Mathematicae et Informaticae, 41 (2013) pp. 175-192.
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
KEYWORD
nonn
AUTHOR
Henry Bottomley, May 28 2003
STATUS
approved