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A190457 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(golden ratio,4,3) and []=floor. 5
3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 0, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 3, 2, 0, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 1, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 0, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 1, 3, 2, 4, 2, 1, 3, 2, 0, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 1, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 3, 2, 0, 3, 1, 4, 2, 1, 3, 2, 4, 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,2,0):  A078588, A005653, A005652

(golden ratio,2,1):  A190427-A190430

(golden ratio,3,0):  A140397-A190400

(golden ratio,3,1):  A140431-A190435

(golden ratio,3,2):  A140436-A190439

(golden ratio,4,c):  A190440-A190461

LINKS

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

MATHEMATICA

r = GoldenRatio; b = 4; c = 3;

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

t = Table[f[n], {n, 1, 320}]

Flatten[Position[t, 0]]

Flatten[Position[t, 1]]

Flatten[Position[t, 2]]

Flatten[Position[t, 3]]

Flatten[Position[t, 4]]

CROSSREFS

Cf. A190458-A190461 and A190463.

Sequence in context: A118874 A208614 A020851 * A179833 A131033 A135821

Adjacent sequences:  A190454 A190455 A190456 * A190458 A190459 A190460

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 10 2011

STATUS

approved

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Last modified February 17 02:33 EST 2019. Contains 320200 sequences. (Running on oeis4.)