Adams, William W.; Davison, J. L. A remarkable class of continued fractions. (English) Zbl 0366.10027 Proc. Am. Math. Soc. 65, 194-198 (1977). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 18 Documents MSC: 11J70 Continued fractions and generalizations 11A63 Radix representation; digital problems PDF BibTeX XML Cite \textit{W. W. Adams} and \textit{J. L. Davison}, Proc. Am. Math. Soc. 65, 194--198 (1977; Zbl 0366.10027) Full Text: DOI OpenURL Online Encyclopedia of Integer Sequences: a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=3. a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=4. a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=10. Decimal expansion of rabbit constant. Partial quotients of the continued fraction of the constant defined by binary sums involving Beatty sequences: c = Sum_{n>=1} 1/2^A049472(n) = Sum_{n>=1} A001951(n)/2^n. Decimal expansion of the constant defined by binary sums involving Beatty sequences: c = Sum_{n>=1} A049472(n)/2^n = Sum_{n>=1} 1/2^A001951(n). Partial quotients of the continued fraction of the constant A119812 defined by binary sums involving Beatty sequences: c = Sum_{n>=1} A049472(n)/2^n = Sum_{n>=1} 1/2^A001951(n). Sturmian word: limit S(infinity) where S(0) = 0, S(1) = 0,1 and for n>=1, S(n+1) = S(n)S(n)S(n-1). a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=5. a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=7. a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=6. a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=8. a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=9. The generalized Fibonacci word f^[3]. The generalized Fibonacci word f^[4]. The generalized Fibonacci word f^[5]. a(n) = 2^Lucas(n). Sturmian word: equals the limit word S(infinity) where S(0) = 0, S(1) = 1 and for n >= 1, S(n+1) = S(n)S(n)S(n)S(n-1). References: [1] J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957. · Zbl 0077.04801 [2] J. L. Davison, A series and its associated continued fraction, Proc. Amer. Math. Soc. 63 (1977), no. 1, 29 – 32. · Zbl 0326.10030 [3] Serge Lang, Introduction to diophantine approximations, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. · Zbl 0144.04005 [4] J. H. Loxton and A. J. van der Poorten, Arithmetic properties of certain functions in several variables. III, Bull. Austral. Math. Soc. 16 (1977), no. 1, 15 – 47. · Zbl 0339.10028 [5] -, Transcendence theory: Advances and applications, Academic Press, New York, 1977, pp. 211-226. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.