OFFSET
1,1
COMMENTS
(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.
FORMULA
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.
EXAMPLE
a(1)=3=L(1+1) because 1=L(1).
a(2)=2 because 2 is not in L.
a(3)=1=L(2-1) because 3=L(2).
a(4)=6=L(3+1) because 4=L(3).
a(6)=4=L(4-1) because 6=L(4).
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 02 2006
STATUS
approved