A188470 a(n) = [5r]-[nr]-[5r-nr], where r=(1+sqrt(5))/2 and []=floor.

1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0

Offset

1

Comments

See A188294.

Essentially the same as 1 - A187946, see formulas. - Michel Dekking, Oct 15 2016, edited by M. F. Hasler, Oct 12 2017

Sequence A188471 lists the position of 0's, all other terms equal 1. - M. F. Hasler, Oct 12 2017

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

a(n) = [5r] - [nr] - [5r-nr], where r=(1+sqrt(5))/2 is the golden ratio.

a(n) = 1 - A187946(n) for n not equal to 5 (from [-x]=-[x]-1 for non-integer x). - Michel Dekking, Oct 15 2016

For n>5, a(n) = 9 - A000201(n) + A000201(n-5). - Max Alekseyev, Oct 14 2017

Maple

A188470 := proc(n)
    8-A000201(n)-A000201(5-n);
end proc:
seq(A188470(n), n=1..50) ; # R. J. Mathar, Oct 13 2017

Mathematica

r = (1 + 5^(1/2))/2 + .0000000000001;
f[n_] := Floor[5r] - Floor[n*r] - Floor[5r - n*r]
t = Flatten[Table[f[n], {n, 1, 200}]] (* A188470 *)
Flatten[Position[t, 0] ]  (* A188471 *)
Flatten[Position[t, 1] ]  (* complement of A188471 *)

Prog

(PARI)
\\ For z = a + b*phi with phi = quadgen(5), exact representation of (sqrt(5)+1)/2:
FLOOR(z, F=1, f(w)=floor(real(z)+imag(z)*w), L=f(F))=while(L!=L=f(F=1+1/F), ); LA188470(n, r=quadgen(5)) = FLOOR(5*r)-FLOOR(n*r)-FLOOR(5*r-n*r) \\ M. F. Hasler, Oct 12 2017
(PARI)
A000201(m) = (sqrtint((m^2)*5)+m)\2;
A188470(n) = if(n<=5, n%5!=0, 9+A000201(n-5)-A000201(n)); \\ Max Alekseyev, Oct 13 2017
(Python)
from math import isqrt
def A188470(n): return 7-(n+isqrt(5*n**2)>>1)+(n-1+isqrt(5*(n-5)**2)>>1) if n>5 else int(n<5) # Chai Wah Wu, Aug 10 2022

Crossrefs

Cf. A188294, A188471, A187946.

Sequence in context: A059095 A187944 A105597 * A333922 A071026 A259022

Adjacent sequences: A188467 A188468 A188469 * A188471 A188472 A188473

Keyword

nonn

Author

Clark Kimberling, Apr 01 2011

Status

approved