|
%I #8 Feb 27 2013 03:35:33
%S 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,
%T 144,76,20,233,123,42,377,19,610,199,68,987,39,1597,322,32,2584,521,
%U 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
%N Transposition sequence of the Wythoff array.
%C 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).
%H Peter J. C. Moses, <a href="/A114579/b114579.txt">Table of n, a(n) for n = 1..10000</a>
%F 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.
%e Start with the northwest corner of the Wythoff array T (A035513):
%e 1 2 3 5 8
%e 4 7 11 18 29
%e 6 10 16 26 42
%e 9 15 24 39 63
%e a(1)=1 because 1=T(1,1) and T(1,1)=1.
%e a(2)=4 because 2=T(1,2) and T(2,1)=4.
%e a(3)=6 because 3=T(1,3) and T(3,1)=6.
%e a(15)=18 because 15=T(4,2) and T(2,4)=18.
%Y Cf. A035513, A114538, A114578.
%K nonn
%O 1,2
%A _Clark Kimberling_, Dec 09 2005
|
