Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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