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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

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OFFSET

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