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A190555 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,2) and []=floor. 5
2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 2, 4, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 1, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 0 (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),2,1):  A190483-A190486

(sqrt(2),3,0):  A190487-A190490

(sqrt(2),3,1):  A190491-A190495

(sqrt(2),3,2):  A190496-A190500

LINKS

Table of n, a(n) for n=1..128.

MATHEMATICA

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

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

t = Table[f[n], {n, 1, 200}] (* A190555 *)

Flatten[Position[t, 0]]          (* A190556 *)

Flatten[Position[t, 1]]          (* A190557 *)

Flatten[Position[t, 2]]          (* A190558 *)

Flatten[Position[t, 3]]          (* A190559 *)

Flatten[Position[t, 4]]          (* A190486 *)

CROSSREFS

Cf. A190556-A190559, A190486.

Sequence in context: A053451 A254076 A257164 * A141843 A130266 A261595

Adjacent sequences:  A190552 A190553 A190554 * A190556 A190557 A190558

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 12 2011

STATUS

approved

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Last modified January 24 04:31 EST 2018. Contains 298115 sequences.