A241575 - OEIS

%I #26 Feb 02 2019 03:17:52

%S 0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,

%T 0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,

%U 1,0,0,1,0

%N Sturmian expansion of 1/2 in base sqrt(2)-1.

%C (a(n)) is an inhomogeneous Sturmian word with the same slope as A159684; the languages of the two infinite words are therefore the same. - _Michel Dekking_, Jun 06 2017

%C (a(n)) is the fixed point of the morphism 0 -> 01010,  1 -> 0101010. - _Michel Dekking_, Feb 02 2019

%H Michel Dekking, <a href="/A241575/b241575.txt">Table of n, a(n) for n = 0..238</a>

%H E. Arthur Robinson, Jr., <a href="https://www.emis.de/journals/INTEGERS/papers/a13num/a13num.Abstract.html">Sturmian expansions and entropy</a>, INTEGERS, Vol. 11B (2011), #A13.

%F a(n) = floor((n+1)*r + t) - floor(n*r + t), where r = sqrt(2)-1, t = 1/2. - _Michel Dekking_, Jun 06 2017

%e 1/2 = .010100101010010100101010010100101001010100101001010100...

%Y Similar to, but different from, A159684.

%K nonn

%O 0

%A _N. J. A. Sloane_, Apr 26 2014

%E More terms from _Michel Dekking_, Jun 06 2017

%E Some terms in data corrected by _Andrew Howroyd_, Feb 22 2018