A241575 Sturmian expansion of 1/2 in base sqrt(2)-1.

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, 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, 1, 0, 0, 1, 0

Offset

0

Comments

(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

(a(n)) is the fixed point of the morphism 0 -> 01010, 1 -> 0101010. - Michel Dekking, Feb 02 2019

Links

Michel Dekking, Table of n, a(n) for n = 0..238

E. Arthur Robinson, Jr., Sturmian expansions and entropy, INTEGERS, Vol. 11B (2011), #A13.

Formula

a(n) = floor((n+1)*r + t) - floor(n*r + t), where r = sqrt(2)-1, t = 1/2. - Michel Dekking, Jun 06 2017

Example

1/2 = .010100101010010100101010010100101001010100101001010100...

Crossrefs

Similar to, but different from, A159684.

Sequence in context: A159684 A244221 A253050 * A285684 A163538 A267188

Adjacent sequences: A241572 A241573 A241574 * A241576 A241577 A241578

Keyword

nonn

Author

N. J. A. Sloane, Apr 26 2014

Extensions

More terms from Michel Dekking, Jun 06 2017

Some terms in data corrected by Andrew Howroyd, Feb 22 2018

Status

approved