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

1,1

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).

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

Mathematica

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

Crossrefs

Cf. A000244 (powers of 3), A079002.

Sequence in context: A239115 A165773 A064414 * A002475 A208281 A306074

Adjacent sequences: A224479 A224480 A224481 * A224483 A224484 A224485

Keyword

nonn,easy

Author

Jonathan Vos Post, Apr 10 2013

Extensions

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

Status

approved