A120752 Numbers k such that {rk} <= c, where r = (1/2)^(1/2), c = 1/2 and { } denotes fractional part.

2, 3, 6, 9, 10, 12, 13, 16, 17, 19, 20, 23, 26, 27, 30, 33, 34, 36, 37, 40, 43, 44, 47, 50, 51, 53, 54, 57, 58, 60, 61, 64, 67, 68, 70, 71, 74, 75, 77, 78, 81, 84, 85, 88, 91, 92, 94, 95, 98, 99, 101, 102, 105, 108, 109, 111, 112, 115, 116, 118, 119, 122, 125, 126, 129, 132

Offset: 1

Author

Clark Kimberling, Jul 01 2006

Keywords

• nonn

Comments

Positions of 0 in A083035.

The sequence is essentially identical to A090892 (see links).

Examples

			(See A120243.)
		

Links

• Sela Fried, Equivalent conditions for the nth element of the Beatty sequence B_sqrt(2) being even, arXiv:2301.00644 [math.HO], 2022.

Crossrefs

Cf. A083035, A120753, A190762.

Programs

Mathematica

r = Sqrt[1/2]; b = 2; c = 0;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A083035 *)
Flatten[Position[t, 0]]      (* A120752 *)
Flatten[Position[t, 1]]      (* A120753 *)