A188082 [nr+kr]-[nr]-[kr], where r=sqrt(3), k=1, [ ]=floor.

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

Offset

1

Comments

The positions of 0 and 1 in this sequence are given by the Beatty sequences A003512 and A003511. See A187950.

This is A188068 shifted one place left.

The trajectory of 0 under the morphism 0 -> 110, 1 -> 1101. - N. J. A. Sloane, Sep 08 2016

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Jeffrey Shallit, Characteristic words as fixed points of homomorphisms, University of Waterloo Technical Report CS-91-72, 1991. See Example 2 with a=1, b=2.

Jeffrey Shallit, Characteristic words as fixed points of homomorphisms. See Example 2 with a=1, b=2. [Cached copy, with permission]

Index entries for sequences that are fixed points of mappings

Formula

a(n)=[nr+r]-[nr]-[kr], where r=sqrt(3).

Mathematica

r=3^(1/2); k=1;
seqA=Table[Floor[n*r+k*r]-Floor[n*r]-Floor[k*r],
{n, 1, 220}]   (* A188082 *)
Flatten[Position[seqA, 0] ] (*A003512*)
Flatten[Position[seqA, 1] ] (*A003511*)

Prog

(Python)
from gmpy2 import isqrt
def A188082(n):
    return int(isqrt(3*(n+1)**2) - isqrt(3*n**2)) - 1 # Chai Wah Wu, Oct 07 2016

Crossrefs

Cf. A187950, A188068.

Sequence in context: A230603 A229343 A085369 * A046980 A152822 A118831

Adjacent sequences: A188079 A188080 A188081 * A188083 A188084 A188085

Keyword

nonn

Author

Clark Kimberling, Mar 20 2011

Status

approved