login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A059648 a(n) = [[(k^2)*n]-(k*[k*n])], where k = sqrt(2) and [] is the floor function. 6
0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The values of (floor((k^2)*j)-(k*(floor(k*j)))) for j=0..20, with k=sqrt(2), are 0, 0.585786, 1.171572, 0.343144, 0.928930, 0.100502, 0.68629, 1.27207, 0.44365, 1.02943, 0.20100, 0.78679, 1.37258, 0.54415, 1.12993, 0.30151, 0.88729, 0.05886, 0.64465, 1.23044, 0.40201
LINKS
MAPLE
Digits := 89; floor_diffs_floored(sqrt(2), 120); floor_diffs_floored := proc(k, upto_n) local j; [seq(floor(floor((k^2)*j)-(k*(floor(k*j)))), j=0..upto_n)]; end;
MATHEMATICA
With[{k = Sqrt[2]}, Table[Floor[Floor[k^2*j] - k*Floor[k*j]], {j, 0, 104}]] (* Jean-François Alcover, Mar 06 2016 *)
PROG
(PARI) for(n=0, 100, print1(floor(floor(n*sqrt(2)^2) - sqrt(2)*floor(n*sqrt(2))), ", ")) \\ G. C. Greubel, Jan 27 2018
(Magma) [Floor(Floor(n*Sqrt(2)^2) - Sqrt(2)*Floor(n*Sqrt(2))): n in [0..100]]; // G. C. Greubel, Jan 27 2018
(Python)
from math import isqrt
def A059648(n): return (m:=n<<1)-1-isqrt(isqrt(n*m)**2<<1) if n else 0 # Chai Wah Wu, Aug 29 2022
CROSSREFS
Cf. A007069. Positions of ones: A059649.
Cf. A002193 (sqrt(2)).
Sequence in context: A188472 A286044 A129272 * A288707 A079261 A354028
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 03 2001
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 29 21:21 EDT 2024. Contains 374734 sequences. (Running on oeis4.)