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Search: id:A084531
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| A084531 |
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Signature sequence of phi = (1+sqrt(5))/2 = 1.61803... |
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+0
7
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
Contribution from Clark Kimberling (ck6(AT)evansville.edu), Oct 31 2009: (Start)
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. (End)
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REFERENCES
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Clark Kimberling, "Fractal Sequences and Interspersions," Ars Combinatoria 45 (1997) 157-168. [From Clark Kimberling (ck6(AT)evansville.edu), Oct 31 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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CROSSREFS
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Cf. A084532.
Adjacent sequences: A084528 A084529 A084530 this_sequence A084532 A084533 A084534
Sequence in context: A058933 A087470 A158456 this_sequence A023129 A007337 A056892
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KEYWORD
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nonn,new
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), May 28 2003
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