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A302253 Positions of 3 in A190436. 5
8, 21, 29, 42, 55, 63, 76, 97, 110, 118, 131, 144, 152, 165, 186, 199, 207, 220, 241, 254, 262, 275, 288, 296, 309, 330, 343, 351, 364, 377, 385, 398, 406, 419, 432, 440, 453, 474, 487, 495, 508, 521, 529, 542, 563, 576, 584, 597, 618, 631, 639, 652, 665, 673, 686, 707, 720, 728 (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):  A140440-A190461

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..20000

MATHEMATICA

r = GoldenRatio; b = 3; c = 2;

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

t = Table[f[n], {n, 1, 500}] (* A190436 *)

Flatten[Position[t, 0]] (* A190437 *)

Flatten[Position[t, 1]] (* A190438 *)

Flatten[Position[t, 2]] (* A190439 *)

Flatten[Position[t, 3]] (* A302253 *)

CROSSREFS

Cf. A190436, A190437, A190438, A190439.

Sequence in context: A271921 A003249 A134862 * A090206 A139590 A154894

Adjacent sequences:  A302250 A302251 A302252 * A302254 A302255 A302256

KEYWORD

nonn

AUTHOR

G. C. Greubel, Apr 04 2018

STATUS

approved

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Last modified July 24 10:55 EDT 2021. Contains 346273 sequences. (Running on oeis4.)