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A190770 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(1/2),3,1) and [ ]=floor. 5
2, 1, 1, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 3, 2, 1, 1, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 0, 2, 1, 1, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 3, 2, 1, 1, 3, 2, 1, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 0, 2, 1, 1, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1, 0, 2, 2, 1, 3, 2, 1, 3, 2, 1, 0, 3, 2, 1, 3, 2, 1 (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 (or b) 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

Table of n, a(n) for n=1..132.

MATHEMATICA

r = Sqrt[1/2]; b = 3; c = 1;

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

t = Table[f[n], {n, 1, 200}] (* A190770 *)

Flatten[Position[t, 0]]      (* A190771 *)

Flatten[Position[t, 1]]      (* A190772 *)

Flatten[Position[t, 2]]      (* A190773 *)

Flatten[Position[t, 3]]      (* A190774 *)

CROSSREFS

Cf. A190771-A190774.

Sequence in context: A325758 A280073 A327523 * A292149 A275676 A025831

Adjacent sequences:  A190767 A190768 A190769 * A190771 A190772 A190773

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 19 2011

STATUS

approved

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Last modified January 19 03:18 EST 2020. Contains 331031 sequences. (Running on oeis4.)