

A114579


Transposition sequence of the Wythoff array.


1



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, 987, 39, 1597, 322, 32, 2584, 521, 110, 4181, 23, 6765, 843, 178, 10946, 63, 17711, 1364, 22, 28657, 2207, 288, 46368, 102, 75025, 3571, 52, 121393, 5778, 466, 196418, 37, 317811, 9349, 754, 514229, 165, 832040, 15127, 28, 1346269, 24476, 1220, 2178309, 267, 3524578, 39603, 84, 5702887, 64079, 1974, 9227465, 25, 14930352, 103682, 3194, 24157817, 432, 39088169, 167761, 136, 63245986, 271443, 5168
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OFFSET

1,2


COMMENTS

A selfinverse permutation of the positive integers. Let s(n)=n1+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).


LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..10000


FORMULA

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.


EXAMPLE

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.


CROSSREFS

Cf. A035513, A114538, A114578.
Sequence in context: A181096 A026239 A171547 * A021220 A195410 A095196
Adjacent sequences: A114576 A114577 A114578 * A114580 A114581 A114582


KEYWORD

nonn


AUTHOR

Clark Kimberling, Dec 09 2005


STATUS

approved



