A224482 Numbers n for which the Lucas numbers modulo n is nondefective (residue complete).

2, 3, 4, 6, 7, 9, 14, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467, 3486784401, 10460353203, 31381059609, 94143178827, 282429536481, 847288609443, 2541865828329, 7625597484987

Offset: 1

Author

Jonathan Vos Post, Apr 10 2013

Keywords

• nonn
• easy

Comments

These are the numbers n = 2, 4, 6, 7, 14, and the powers of 3 (without 3^0=1).

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..2100
• B. Avila and Y. Chen, On moduli for which the Lucas numbers contain a complete residue system, Fibonacci Quarterly, 51 (2013), 151-152.
• Cheng Lien Lang and Mong Lung Lang, Fibonacci system and residue completeness, arXiv:1304.2892 [math.NT], 2013.
• Index entries for linear recurrences with constant coefficients, signature (3).

Crossrefs

Cf. A000244 (powers of 3), A079002.

Programs

Mathematica

With[{nn = 27}, Union[TakeWhile[{2, 4, 6, 7, 14}, # <= 3^nn &], Array[3^# &, nn]]] (* Michael De Vlieger, Oct 06 2020 *)

Formula

G.f.: x*(15*x^7+13*x^6+12*x^5+11*x^4+6*x^3+5*x^2+3*x-2) / (3*x-1). - Colin Barker, Apr 14 2013

Extensions

Corrected (term 9 was 27), Joerg Arndt, Apr 14 2013