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

1,1

Comments

Positions of 0 in A083035.

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

Links

Table of n, a(n) for n=1..66.

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

Example

(See A120243.)

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 *)

Crossrefs

Cf. A083035, A120753, A190762.

Sequence in context: A032938 A188323 A090892 * A236759 A134695 A323393

Adjacent sequences: A120749 A120750 A120751 * A120753 A120754 A120755

Keyword

nonn

Author

Clark Kimberling, Jul 01 2006

Status

approved