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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 (list; graph; refs; listen; history; text; internal format)
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

G. C. Greubel, Table of n, a(n) for n = 1..10000

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

Cf. A190670, A190671.

Sequence in context: A071004 A188083 A102560 * A285258 A068428 A078650

Adjacent sequences:  A190666 A190667 A190668 * A190670 A190671 A190672

KEYWORD

nonn,changed

AUTHOR

Clark Kimberling, May 16 2011

STATUS

approved

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Last modified September 16 09:08 EDT 2019. Contains 327093 sequences. (Running on oeis4.)