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A190483 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),2,1) and []=floor. 24
1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

(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

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

MATHEMATICA

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

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

t = Table[f[n], {n, 1, 200}]  (* A190483 *)

Flatten[Position[t, 0]]   (* A190484 *)

Flatten[Position[t, 1]]   (* A190485 *)

Flatten[Position[t, 2]]   (* A190486 *)

PROG

(Python)

from sympy import sqrt, floor

r=sqrt(2)

def a(n): return floor((2*n + 1)*r) - 2*floor(n*r) - floor(r)

print [a(n) for n in range(1, 501)] # Indranil Ghosh, Jul 02 2017

CROSSREFS

Cf. A190484, A190485, A190486.

Sequence in context: A257024 A124433 A287104 * A090239 A165276 A035698

Adjacent sequences:  A190480 A190481 A190482 * A190484 A190485 A190486

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 11 2011

STATUS

approved

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)