A189379 n+[nr/t]+[ns/t]; r=2, s=(-1+sqrt(5))/2, t=(1+sqrt(5))/2.

2, 4, 7, 9, 12, 15, 17, 20, 23, 25, 28, 30, 33, 36, 38, 41, 44, 46, 49, 51, 54, 57, 59, 62, 64, 67, 70, 72, 75, 78, 80, 83, 85, 88, 91, 93, 96, 98, 101, 104, 106, 109, 112, 114, 117, 119, 122, 125, 127, 130, 133, 135, 138, 140, 143, 146, 148, 151, 153, 156, 159, 161, 164, 167, 169, 172, 174, 177, 180, 182, 185, 187, 190, 193, 195, 198, 201, 203, 206, 208, 211, 214, 216, 219

Offset: 1

Author

Clark Kimberling, Apr 20 2011

Keywords

• nonn

Comments

(Conjecture) These are the numbers n such that (n+1)-sections of the Fibonacci word contain both "000" and "111". - Don Reble, Apr 07 2021

Conjecture proved April 8 2021 using the Walnut theorem prover. - Jeffrey Shallit, Apr 09 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, A189378.

Programs

Mathematica

(See A189377.)