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A188037 a(n) = floor(nr) - 1 - floor((n-1)r), where r = sqrt(2). 6
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 (list; graph; refs; listen; history; text; internal format)
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.

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.

Sequence in context: A287931 A289074 A289242 * A144598 A144606 A060510

Adjacent sequences:  A188034 A188035 A188036 * A188038 A188039 A188040

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 19 2011

STATUS

approved

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Last modified March 26 00:29 EDT 2019. Contains 321479 sequences. (Running on oeis4.)