A224482 - OEIS

%I #49 Jan 05 2025 19:51:40

%S 2,3,4,6,7,9,14,27,81,243,729,2187,6561,19683,59049,177147,531441,

%T 1594323,4782969,14348907,43046721,129140163,387420489,1162261467,

%U 3486784401,10460353203,31381059609,94143178827,282429536481,847288609443,2541865828329,7625597484987

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

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

%H Michael De Vlieger, <a href="/A224482/b224482.txt">Table of n, a(n) for n = 1..2100</a>

%H B. Avila and Y. Chen, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/51-2/AvilaChen.pdf">On moduli for which the Lucas numbers contain a complete residue system</a>, Fibonacci Quarterly, 51 (2013), 151-152.

%H Cheng Lien Lang and Mong Lung Lang, <a href="http://arxiv.org/abs/1304.2892">Fibonacci system and residue completeness</a>, arXiv:1304.2892 [math.NT], 2013.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (3).

%F 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

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

%Y Cf. A000244 (powers of 3), A079002.

%K nonn,easy

%O 1,1

%A _Jonathan Vos Post_, Apr 10 2013

%E Corrected (term 9 was 27), _Joerg Arndt_, Apr 14 2013