A189378 a(n) = n + [nr/s] + [nt/s]; r=2, s=(-1+sqrt(5))/2, t=(1+sqrt(5))/2.

6, 13, 19, 26, 34, 40, 47, 53, 61, 68, 74, 81, 89, 95, 102, 108, 116, 123, 129, 136, 142, 150, 157, 163, 170, 178, 184, 191, 197, 205, 212, 218, 225, 233, 239, 246, 252, 259, 267, 273, 280, 286, 294, 301, 307, 314, 322, 328, 335, 341, 349, 356, 362, 369, 375, 383, 390, 396, 403, 411, 417, 424, 430, 438, 445, 451, 458, 466, 472, 479, 485, 492, 500, 506, 513, 519, 527, 534, 540, 547, 555, 561

Offset: 1

Author

Clark Kimberling, Apr 20 2011

Keywords

• nonn

Comments

Theorem: These are the numbers k such that (k+1)-sections of the Fibonacci word contain neither "000" nor "111". Proved by J. Shallit and "Walnut", Apr 06 2021. - Don Reble, Apr 06 2021

Links

• Luke Schaeffer, Jeffrey Shallit, and Stefan Zorcic, Beatty Sequences for a Quadratic Irrational: Decidability and Applications, arXiv:2402.08331 [math.NT], 2024. See pp. 11-12.

Crossrefs

Cf. A189377, A189379.

Cf. A001622, A094214.

See also A339950.

Programs

Mathematica

(See A189377.)