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A190886 a(n) = [5nr]-5[nr], where r=sqrt(5). 6
1, 2, 3, 4, 0, 2, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 2, 3, 4, 0, 1, 3, 4, 0, 1, 2, 3, 0, 1, 2, 3, 4, 1, 2, 3, 4, 0, 1, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3, 4, 1, 2, 3, 4, 0, 2, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3, 4, 1, 2, 3, 4, 0, 2, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3, 0, 1, 2, 3, 4, 0, 2, 3, 4, 0, 1, 3, 4, 0, 1, 2, 3, 0, 1, 2, 3, 4, 1, 2, 3, 4, 0, 1, 3, 4, 0, 1, 2, 4, 0, 1, 2, 3, 4, 1, 2, 3, 4, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In general, suppose that 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.  For c=0, there are b of these position sequences, and they comprise a partition of the positive integers.

LINKS

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

FORMULA

a(n) = [5nr]-5[nr], where r=sqrt(5).

MATHEMATICA

r = Sqrt[5];

f[n_] := Floor[5n*r] - 5*Floor[n*r]

t = Table[f[n], {n, 1, 400}] (* A190886 *)

Flatten[Position[t, 0]]      (* A190887 *)

Flatten[Position[t, 1]]      (* A190888 *)

Flatten[Position[t, 2]]      (* A190889 *)

Flatten[Position[t, 3]]      (* A190890 *)

Flatten[Position[t, 4]]      (* A190891 *)

CROSSREFS

Cf. A190887, A190888, A190889, A190890, A190891.

Sequence in context: A060511 A082853 A230431 * A257845 A162593 A279125

Adjacent sequences:  A190883 A190884 A190885 * A190887 A190888 A190889

KEYWORD

nonn

AUTHOR

Clark Kimberling, May 26 2011

STATUS

approved

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Last modified December 5 20:39 EST 2021. Contains 349558 sequences. (Running on oeis4.)