A115094 Permutation of N based on lower Wythoff sequence.

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, 29, 28, 27, 32, 31, 30, 35, 34, 33, 36, 38, 37, 39, 42, 41, 40, 45, 44, 43, 48, 47, 46, 49, 51, 50, 52, 55, 54, 53, 58, 57, 56, 61, 60, 59, 62, 64, 63, 65, 67, 66, 68, 71, 70, 69, 74

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.

Links

Table of n, a(n) for n=1..72.

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

Cf. A000201, A001950, A002251.

Sequence in context: A194761 A129674 A120771 * A165958 A113655 A177977

Adjacent sequences: A115091 A115092 A115093 * A115095 A115096 A115097

Keyword

nonn

Author

Clark Kimberling, Mar 02 2006

Status

approved