A130526 A permutation of the integers induced by the lower and upper Wythoff sequences.

0, 1, -1, 2, 3, -2, 4, -3, 5, 6, -4, 7, 8, -5, 9, -6, 10, 11, -7, 12, -8, 13, 14, -9, 15, 16, -10, 17, -11, 18, 19, -12, 20, 21, -13, 22, -14, 23, 24, -15, 25, -16, 26, 27, -17, 28, 29, -18, 30, -19, 31, 32, -20, 33, -21, 34, 35, -22, 36, 37, -23, 38, -24, 39, 40, -25, 41, 42, -26

Offset

0,4

Comments

Another permutation of the integers is -A130526.

Links

Table of n, a(n) for n=0..68.

Formula

a(0) = 0; a(n)=k if n=L(k); a(n)=-k if n=U(k), where L(k) = A000201(k)=Floor(n*phi) = Lower Wythoff sequence, U(k) = A001950(k) = k+L(k) = Upper Wythoff sequence.

Example

6=L(4), so a(6)=4.
7=U(3), so a(7)=-3.

Crossrefs

Cf. A000201, A001950, A026242, A130527.

Sequence in context: A214371 A026338 A026242 * A351955 A174523 A363159

Adjacent sequences: A130523 A130524 A130525 * A130527 A130528 A130529

Keyword

sign

Author

Clark Kimberling, Jun 02 2007

Status

approved