A188082 - OEIS

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

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OFFSET

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)