A130527 A permutation of the integers induced by the Beatty sequence for sqrt(2).

0, 1, 2, -1, 3, 4, -2, 5, 6, 7, -3, 8, 9, -4, 10, 11, 12, -5, 13, 14, -6, 15, 16, -7, 17, 18, 19, -8, 20, 21, -9, 22, 23, 24, -10, 25, 26, -11, 27, 28, -12, 29, 30, 31, -13, 32, 33, -14, 34, 35, 36, -15, 37, 38, -16, 39, 40, 41, -17, 42, 43, -18, 44, 45, -19, 46, 47, 48

Offset: 0

Author

Clark Kimberling, Jun 02 2007

Keywords

• sign

Comments

Another permutation of the integers is -A130527.

Examples

			5=L(4), so a(5)=4.
6=U(2), so a(6)=-2.
		

Crossrefs

Cf. A001951, A001952, A130526.

Formula

a(0)=0; a(n)=k if n=L(k); a(n)=-k if n=U(k), where L(k) = A001951(k) = Floor(k*sqrt(2)), U(k) = A001952(k) = 2k+L(k).