A097508 a(n) = floor(n*(sqrt(2)-1)).
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
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
- 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.
Programs
-
Magma
[Floor(n*Sqrt(2)) - n: n in [0..100]]; // G. C. Greubel, Mar 27 2018
-
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 *) -
PARI
a(n)=sqrtint(2*n^2)-n \\ Charles R Greathouse IV, Sep 02 2015
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
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
Comments