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 A188037 a(n) = floor(nr) - 1 - floor((n-1)r), where r = sqrt(2). 16
 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. 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 FrÃ¶hlich, 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

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Last modified August 9 00:15 EDT 2022. Contains 356016 sequences. (Running on oeis4.)