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A097508 a(n) = floor(n*(sqrt(2)-1)). 7
0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29, 29, 30, 30, 31, 31, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
Old name was: Differences between floor(n*sqrt(2)) and n.
LINKS
Heinz H. Bauschke, Minh N. Dao, and Scott B. Lindstrom, The Douglas-Rachford algorithm for a hyperplane and a doubleton, arXiv:1804.08880 [math.OC], 2018.
Marcel Celaya and Frank Ruskey, Morphic Words and Nested Recurrence Relations, arXiv preprint arXiv:1307.0153 [math.CO], 2013.
Luke Schaeffer, Jeffrey Shallit, and Stefan Zorcic, Beatty Sequences for a Quadratic Irrational: Decidability and Applications, arXiv:2402.08331 [math.NT], 2024. See pp. 17-18.
FORMULA
a(n) = (floor(n / cos(45 degrees))) - n.
a(n) = A001951(n) - n. - R. J. Mathar, Sep 19 2010
a(n) = floor((sqrt(2)-1)*n). [Celaya-Ruskey] - N. J. A. Sloane, Nov 14 2013
a(2*n) = 2*a(n) + A197879(n). - Robert Israel, Aug 21 2014
MAPLE
seq(floor(n*sqrt(2)) - n, n = 0 .. 100); # Robert Israel, Aug 21 2014
MATHEMATICA
Table[Floor[n Sqrt[2]]-n, {n, 0, 80}] (* Harvey P. Dale, Dec 04 2014 *)
PROG
(PARI) a(n)=sqrtint(2*n^2)-n \\ Charles R Greathouse IV, Sep 02 2015
(Magma) [Floor(n*Sqrt(2)) - n: n in [0..100]]; // G. C. Greubel, Mar 27 2018
CROSSREFS
Sequence in context: A172476 A172267 A231151 * A244225 A109964 A247366
KEYWORD
easy,nonn
AUTHOR
Odimar Fabeny, Aug 26 2004
EXTENSIONS
Extended by R. J. Mathar, Sep 19 2010
Definition edited by Robert Israel, Aug 21 2014
Name changed by Michel Dekking, Jul 01 2023
STATUS
approved

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Last modified March 19 06:05 EDT 2024. Contains 370952 sequences. (Running on oeis4.)