A188433 a(n) = [2r]-[nr]-[2r-nr], where r=(1+sqrt(5))/2 and [.]=floor.

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

Offset

1

Comments

This is column two of the array A188294.

a(n) = 1 - A123740(n-2) for n>2 (from [-x] = -[x] - 1 for non-integer x). - Michel Dekking, Oct 03 2016

Positions of 0's and 1's are given in A188434 (essentially = A101868) and A188435 (essentially = A188010). 0's are always isolated, and except for the initial term, run lengths of 1's are either 2 or 4. In that sequence of run lengths (1, 2, 4, 2, 4, 4, 2, 4, 2, ...), the 2's are always isolated and the run lengths of 4's are either 1 or 2. In that sequence of run lengths (1, 2, 1, 2, 2, 1, 2, 1, 2, 2, ...), 1's are always isolated, and the run lengths of 2's are again either 1 or 2. - M. F. Hasler, Oct 12 2017

Along the same line of Dekking's comment above, a(n) = 1 - A188009(n), for n > 2. This explains why A188435(n) = A188010(n+1) and A188434(n) = A101868(n+1) = A101866(1,n+1) for all n > 1. - M. F. Hasler, Dec 14 2017

Links

Table of n, a(n) for n=1..138.

Formula

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

Mathematica

r = (1 + 5^(1/2))/2;
f[n_] := Floor[2r] - Floor[n*r] - Floor[2r - n*r]
A188433 = Flatten[Table[f[n], {n, 1, 200}]] (* see also A188434 and A188435 *)

Prog

(PARI) a(n, a=sqrt(5)/2-.5)=3-n\a-(2-n)\a \\ M. F. Hasler, Oct 12 2017

Crossrefs

Cf. A188294, A188434, A188435, A188009.

Sequence in context: A117568 A093521 A187948 * A267635 A267034 A167364

Adjacent sequences: A188430 A188431 A188432 * A188434 A188435 A188436

Keyword

nonn

Author

Clark Kimberling, Mar 31 2011

Status

approved