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
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Mar 19 2011.
STATUS
approved