A188037 a(n) = floor(nr) - 1 - floor((n-1)r), where r = sqrt(2).

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

Offset

1

Comments

Is this A159684 with an additional 0 in front? - R. J. Mathar, Mar 20 2011

The answer is yes, since it follows right from the definitions of the sequences that (a(n)) is equal to A159684 with a different offset. - Michel Dekking, Jan 31 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Heinz H. Bauschke, Minh N. Dao, Scott B. Lindstrom, The Douglas-Rachford algorithm for a hyperplane and a doubleton, arXiv:1804.08880 [math.OC], 2018.

N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Formula

a(n) = floor(nr) - floor(r) - floor(nr - r), where r = sqrt(2).

Mathematica

r=2^(1/2)); k=1;
t=Table[Floor[n*r]-Floor[(n-k)*r]-Floor[k*r], {n, 1, 220}]
Table[Floor[n Sqrt[2]] - Floor[Sqrt[2]] - Floor[n Sqrt[2] - Sqrt[2]], {n, 100}] (* Vincenzo Librandi, Jan 31 2017 *)

Prog

(Magma) [Floor(n*Sqrt(2))-Floor(Sqrt(2))-Floor(n*Sqrt(2)- Sqrt(2)): n in [1..100]]; // Vincenzo Librandi, Jan 31 2017
(PARI) a(n) = floor(n*sqrt(2))-1-floor((n-1)*sqrt(2)) \\ Felix Fröhlich, Jan 31 2017

Crossrefs

Cf. A080754, A083088, A188014, A188037, A188038.

A159684 is an essentially identical sequence.

The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A003151 as the parent: A003151, A001951, A001952, A003152, A006337, A080763, A082844 (conjectured), A097509, A159684, A188037, A245219 (conjectured), A276862. - N. J. A. Sloane, Mar 09 2021

Sequence in context: A289074 A289242 A346218 * A144598 A144606 A060510

Adjacent sequences: A188034 A188035 A188036 * A188038 A188039 A188040

Keyword

nonn

Author

Clark Kimberling, Mar 19 2011.

Status

approved