A263844 Constant term in expansion of n in Fraenkel's exotic ternary representation.
0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 0, 1, 2
Offset: 1
Keywords
Examples
See the link to Table 2 of Fraenkel (2000).
Links
- Michel Dekking, Table of n, a(n) for n = 1..5000
- Aviezri S. Fraenkel, On the recurrence f(m+1)= b(m)*f(m)-f(m-1) and applications, Discrete Mathematics 224 (2000), pp. 273-279.
- A. S. Fraenkel, An exotic ternary representation of the first few positive integers (Table 2 from Fraenkel (2000).)
- F. Michel Dekking, Morphisms, Symbolic Sequences, and Their Standard Forms, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.1.
Programs
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Magma
[Floor((n+2)*(1-1/Sqrt(2)))+Floor((n+1)*(1-1/Sqrt(2)))- 2*Floor(n*(1-1/Sqrt(2))): n in [1..100]]; // Vincenzo Librandi, Feb 12 2018
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Mathematica
Table[Floor[(n + 2) (1 - 1/Sqrt[2])] + Floor[(n + 1) (1 - 1/Sqrt[2])] - 2 Floor[n (1 - 1/Sqrt[2])], {n, 100}] (* Vincenzo Librandi, Feb 12 2018 *)
Formula
a(n) = floor((n+2)r) + floor((n+1)r) - 2*floor(nr), where r = 1 - 1/sqrt(2). - Michel Dekking, Feb 11 2018
Extensions
More terms and new offset from Michel Dekking, Feb 11 2018
Comments