

A190496


a(n) = [(bn+c)r]b[nr][cr], where (r,b,c)=(sqrt(2),3,2) and []=floor.


25



2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 3, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 3, 2, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 3, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 3, 2, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 0
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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<=b1, 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): A190427A190430
(sqrt(2),2,0): A190480
(sqrt(2),2,1): A190483A190486
(sqrt(2),3,0): A190487A190490
(sqrt(2),3,1): A190491A190495
(sqrt(2),3,2): A190496A190500


LINKS

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


MATHEMATICA

r = Sqrt[2]; b = 3; c = 2;
f[n_] := Floor[(b*n + c)*r]  b*Floor[n*r]  Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190496 *)
Flatten[Position[t, 0]] (* A190497 *)
Flatten[Position[t, 1]] (* A190498 *)
Flatten[Position[t, 2]] (* A190499 *)
Flatten[Position[t, 3]] (* A190500 *)


CROSSREFS

Cf. A190497, A190498, A190499, A190500.
Sequence in context: A076423 A075660 A270788 * A193926 A211450 A073058
Adjacent sequences: A190493 A190494 A190495 * A190497 A190498 A190499


KEYWORD

nonn


AUTHOR

Clark Kimberling, May 11 2011


STATUS

approved



