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A190669
a(n) = [(b*n+c)*r] - b*[n*r] - [c*r], where (r,b,c)=(sqrt(3),2,0) and [ ] = floor.
4
1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1
OFFSET
1
COMMENTS
Write a(n) = [(b*n+c)*r] - b*[n*r] - [c*r]. If r>0 and b and c are integers satisfying b >= 2 and 0 <= c <= b-1, then 0 <= a(n) <= b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b. These b+1 position sequences comprise a partition of the positive integers.
Examples:
(golden ratio,2,1): A190427-A190430
(sqrt(2),2,0): A197879, A120243, A120749
(sqrt(2),2,1): A190483-A190486
(sqrt(2),3,0): A190487-A190490
(sqrt(2),3,1): A190491-A190495
(sqrt(2),3,2): A190496-A190500
(sqrt(2),4,c): A190544-A190566
(sqrt(3),2,0): A190669-A190671
LINKS
FORMULA
a(n) = floor(2*n*sqrt(3)) - 2*floor(n*sqrt(3)).
MATHEMATICA
r = Sqrt[3]; b = 2; c = 0;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190669 *)
Flatten[Position[t, 0]] (* A190670 *)
Flatten[Position[t, 1]] (* A190671 *)
PROG
(PARI) for(n=1, 100, print1(floor(2*n*sqrt(3)) - 2*floor(n*sqrt(3)), ", ")) \\ G. C. Greubel, Apr 20 2018
(Magma) [Floor(2*n*Sqrt(3)) - 2*Floor(n*Sqrt(3)): n in [1..100]]; // G. C. Greubel, Apr 20 2018
CROSSREFS
Sequence in context: A071004 A188083 A102560 * A355328 A285258 A068428
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 16 2011
STATUS
approved