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%I #26 Apr 06 2020 01:33:08
%S 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,
%T 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,
%U 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
%N Signature sequence of phi = (1+sqrt(5))/2 = 1.61803...
%C 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.
%C 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
%D Clark Kimberling, "Fractal Sequences and Interspersions," Ars Combinatoria 45 (1997) 157-168.
%H T. D. Noe, <a href="/A084531/b084531.txt">Table of n, a(n) for n = 1..1000</a>
%H Glen Joyce C. Dulatre, Jamilah V. Alarcon, Vhenedict M. Florida, Daisy Ann A. Disu, <a href="http://www.dmmmsu-sluc.com/wp-content/uploads/2018/03/CAS-Monitor-2016-2017-1.pdf">On Fractal Sequences</a>, DMMMSU-CAS Science Monitor (2016-2017) Vol. 15 No. 2, 109-113.
%H Casey Mongoven, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_41_from175to192.pdf">Sonification of multiple Fibonacci-related sequences</a>, Annales Mathematicae et Informaticae, 41 (2013) pp. 175-192.
%t 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 *)
%Y Cf. A084532, A167267.
%K nonn
%O 1,2
%A _Henry Bottomley_, May 28 2003
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