A188082 - OEIS

%I #28 Feb 08 2017 02:11:19

%S 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,

%T 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,

%U 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

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

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

%C This is A188068 shifted one place left.

%C The trajectory of 0 under the morphism 0 -> 110, 1 -> 1101. - _N. J. A. Sloane_, Sep 08 2016

%H Chai Wah Wu, <a href="/A188082/b188082.txt">Table of n, a(n) for n = 1..10000</a>

%H Jeffrey Shallit, <a href="http://cs.uwaterloo.ca/~shallit/papers.html">Characteristic words as fixed points of homomorphisms</a>, University of Waterloo Technical Report CS-91-72, 1991. See Example 2 with a=1, b=2.

%H Jeffrey Shallit, <a href="/A005614/a005614.ps">Characteristic words as fixed points of homomorphisms</a>. See Example 2 with a=1, b=2. [Cached copy, with permission]

%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>

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

%t r=3^(1/2); k=1;

%t seqA=Table[Floor[n*r+k*r]-Floor[n*r]-Floor[k*r],

%t {n,1,220}]   (* A188082 *)

%t Flatten[Position[seqA,0] ] (*A003512*)

%t Flatten[Position[seqA,1] ] (*A003511*)

%o (Python)

%o from gmpy2 import isqrt

%o def A188082(n):

%o     return int(isqrt(3*(n+1)**2) - isqrt(3*n**2)) - 1 # _Chai Wah Wu_, Oct 07 2016

%Y Cf. A187950, A188068.

%K nonn

%O 1

%A _Clark Kimberling_, Mar 20 2011