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A190549 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,1) and []=floor. 6
2, 3, 1, 3, 0, 2, 4, 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, 4, 1, 3, 1, 2, 4, 2, 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, 4, 2, 3, 1, 3, 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, 4, 1, 3, 1, 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, 4, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

G. C. Greubel, Table of n, a(n) for n = 1..1000

MATHEMATICA

r = Sqrt[2]; b = 4; c = 1;

f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];

t = Table[f[n], {n, 1, 200}] (* A190549 *)

Flatten[Position[t, 0]]          (* A190550 *)

Flatten[Position[t, 1]]          (* A190551 *)

Flatten[Position[t, 2]]          (* A190552 *)

Flatten[Position[t, 3]]          (* A190553 *)

Flatten[Position[t, 4]]          (* A190554 *)

CROSSREFS

Cf. A190550, A190551, A190552, A190553.

Sequence in context: A025258 A118846 A082503 * A064442 A287566 A134411

Adjacent sequences:  A190546 A190547 A190548 * A190550 A190551 A190552

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 12 2011

STATUS

approved

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Last modified August 3 04:47 EDT 2021. Contains 346435 sequences. (Running on oeis4.)