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A190561 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,3) and []=floor. 6
1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Write a(n)=[(bn+c)r]-b[nr]-[cr]. 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): A190480-A190482
(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
LINKS
MATHEMATICA
r = Sqrt[2]; b = 4; c = 3;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190561 *)
Flatten[Position[t, 0]] (* A190562 *)
Flatten[Position[t, 1]] (* A190563 *)
Flatten[Position[t, 2]] (* A190564 *)
Flatten[Position[t, 3]] (* A190565 *)
Flatten[Position[t, 4]] (* A190566 *)
CROSSREFS
Sequence in context: A211356 A176107 A327852 * A359793 A074735 A074090
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 12 2011
STATUS
approved

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Last modified June 19 19:59 EDT 2024. Contains 373507 sequences. (Running on oeis4.)