Stolarsky, Kenneth B. Beatty sequences, continued fractions, and certain shift operators. (English) Zbl 0359.10028 Can. Math. Bull. 19, 473-482 (1976). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 51 Documents MSC: 11J70 Continued fractions and generalizations 11B37 Recurrences 11B34 Representation functions Keywords:Bibliography × Cite Format Result Cite Review PDF Full Text: DOI Online Encyclopedia of Integer Sequences: Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622. Upper Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi^2), where phi = (1+sqrt(5))/2. The binary complement of the infinite Fibonacci word A003849. Start with 1, apply 0->1, 1->10, iterate, take limit. a(n) is the concatenation of a(n-1) and a(n-2) with a(1)=1, a(2)=2. a(n) is formed by concatenating a(n-2) and a(n-1), with a(0) = 1, a(1) = 2;