A083035 a(n) = floor(sqrt(2)*n)-2*floor(n/sqrt(2)).

1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Benoit Cloitre, Fractal walk starting at (0,0) with step of unit length turning right if a(n)=0 and left otherwise for n=1 up to 10^6

Sela Fried, The beauty of Beatty sequences.

Formula

a(n) = floor(n*sqrt(2)) mod 2. - T. D. Noe, Oct 11 2006

Mathematica

Table[Floor[Sqrt[2]n]-2Floor[n/Sqrt[2]], {n, 120}] (* Harvey P. Dale, Mar 08 2017 *)
Table[Mod[Floor[Sqrt[2] n], 2], {n, 120}] (* IWABUCHI Yu(u)ki, May 01 2020 *)

Prog

(PARI) a(n)=sqrtint(2*n^2)%2 \\ Charles R Greathouse IV, Oct 14 2013

Crossrefs

Cf. A083036, A083037, A083038, A001951 (floor(n*sqrt(2))).

Sequence in context: A372574 A028863 A089012 * A359422 A356161 A187074

Adjacent sequences: A083032 A083033 A083034 * A083036 A083037 A083038

Keyword

nonn,easy

Author

Benoit Cloitre, Apr 17 2003

Status

approved