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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

G. C. Greubel, Table of n, a(n) for n = 0..10000

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-Fran├žois 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

CROSSREFS

Positions of ones: A059649.

Sequence in context: A188472 A286044 A129272 * A288707 A079261 A285495

Adjacent sequences:  A059645 A059646 A059647 * A059649 A059650 A059651

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 03 2001

STATUS

approved

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Last modified January 17 06:41 EST 2019. Contains 319207 sequences. (Running on oeis4.)