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%I #3 Mar 30 2012 18:57:06
%S 3,2,1,6,5,4,7,9,8,10,12,11,13,16,15,14,19,18,17,20,22,21,23,25,24,26,
%T 29,28,27,32,31,30,35,34,33,36,38,37,39,42,41,40,45,44,43,48,47,46,49,
%U 51,50,52,55,54,53,58,57,56,61,60,59,62,64,63,65,67,66,68,71,70,69,74
%N Permutation of N based on lower Wythoff sequence.
%C (1) a(n)=n if and only if n is in the upper Wythoff sequence, A001950. (2) This is a self-inverse permutation of N. (3) a(n)-n is one of -2,-1,0,1,2 for every n and each of these occurs infinitely many times. (4) The sequence a(n)-n is a nonperiodic tiling of N.
%F Let L be the lower Wythoff sequence, A000201. Then a(n)=n if n is not any L(k), a(n)=L(k+1) if n=L(k) for odd k, a(n)=L(k-1) if n=L(k) for even k.
%e a(1)=3=L(1+1) because 1=L(1).
%e a(2)=2 because 2 is not in L.
%e a(3)=1=L(2-1) because 3=L(2).
%e a(4)=6=L(3+1) because 4=L(3).
%e a(6)=4=L(4-1) because 6=L(4).
%Y Cf. A000201, A001950, A002251.
%K nonn
%O 1,1
%A _Clark Kimberling_, Mar 02 2006
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