A114579 Transposition sequence of the Wythoff array.

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

Offset

1,2

Comments

A self-inverse permutation of the positive integers. Let s(n)=n-1+Floor(n*tau) and F(n)=n-th 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