%I #23 Sep 08 2022 08:44:57

%S 0,5,7,8,13,15,16,21,23,24,29,31,32,37,39,40,45,47,48,53,55,56,61,63,

%T 64,69,71,72,77,79,80,85,87,88,93,95,96,101,103,104,109,111,112,117,

%U 119,120,125,127,128,133,135,136,141,143,144,149,151,152,157,159

%N Numbers that are congruent to {0, 5, 7} mod 8.

%C Numbers m such that Lucas(m) mod 3 = 2. - _Bruno Berselli_, Oct 19 2017

%H Vincenzo Librandi, <a href="/A047477/b047477.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).

%F G.f.: x^2*(5+2*x+x^2)/((1-x)^2*(1+x+x^2)). - _Colin Barker_, May 14 2012

%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. - _Vincenzo Librandi_, May 16 2012

%F From _Wesley Ivan Hurt_, Jun 10 2016: (Start)

%F a(n) = (24*n - 12 + 3*cos(2*n*Pi/3) - 7*sqrt(3)*sin(2*n*Pi/3))/9.

%F a(3*k) = 8*k-1, a(3*k-1) = 8*k-3, a(3*k-2) = 8*k-8. (End)

%p A047477:=n->(24*n-12+3*cos(2*n*Pi/3)-7*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047477(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016

%t Select[Range[0, 300], MemberQ[{0, 5, 7}, Mod[#, 8]] &] (* _Vincenzo Librandi_, May 16 2012 *)

%o (Magma) I:=[0, 5, 7, 8]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]; // _Vincenzo Librandi_, May 16 2012

%Y Cf. A000032.

%Y Cf. A016825: numbers m such that Lucas(m) mod 3 = 0.

%Y Cf. A047459: numbers m such that Lucas(m) mod 3 = 1.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_