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Search: id:A114579
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| A114579 |
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Transposition sequence of the Wythoff array. |
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1
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| 1, 4, 6, 2, 9, 3, 7, 12, 5, 11, 10, 8, 14, 13, 18, 16, 21, 15, 34, 29, 17, 55, 47, 26, 89, 24, 144, 76, 20, 233, 123, 42, 377, 19, 610, 199, 68, 910, 39, 1210, 322, 32, 1510, 521, 110, 1810, 23, 2110, 821, 178, 2410, 63, 1121, 22, 1421, 288, 102, 1721, 52
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A self-inverse permutation of the positive integers. Let s(n)=n-1+Floor(n*tau) and F(n)=nth Fibonacci number. Then F(n+1) is in position s(n), and s(n) is in position F(n+1).
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FORMULA
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Suppose (as at A114538) that T is a rectangular array consisting of all the positive integers, each exactly once. The transposition sequence of T is obtained by placing T(i, j) in position T(j, i) for all i and j.
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EXAMPLE
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Start with the northwest corner of the Wythoff array T (A035513):
1 2 3 5 8
4 7 11 18 29
6 10 16 26 42
9 15 24 39 63
a(1)=1 because 1=T(1,1) and T(1,1)=1.
a(2)=4 because 2=T(1,2) and T(2,1)=4.
a(3)=6 because 3=T(1,3) and T(3,1)=6.
a(15)=18 because 15=T(4,2) and T(2,4)=18.
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CROSSREFS
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Cf. A035513, A114538, A114578.
Sequence in context: A088516 A114538 A026239 this_sequence A021220 A095196 A074828
Adjacent sequences: A114576 A114577 A114578 this_sequence A114580 A114581 A114582
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Dec 09 2005
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