A047339 - OEIS

%I #21 Sep 08 2022 08:44:57

%S 2,3,4,9,10,11,16,17,18,23,24,25,30,31,32,37,38,39,44,45,46,51,52,53,

%T 58,59,60,65,66,67,72,73,74,79,80,81,86,87,88,93,94,95,100,101,102,

%U 107,108,109,114,115,116,121,122,123,128,129,130,135,136,137,142

%N Numbers that are congruent to {2, 3, 4} mod 7.

%H Vincenzo Librandi, <a href="/A047339/b047339.txt">Table of n, a(n) for n = 1..3000</a>

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

%F a(n+1) = 7*floor(n/3)+(n mod 3)+2. - _Gary Detlefs_, Mar 09 2010

%F G.f.: x*(2+x+x^2+3*x^3)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 04 2011

%F From _Wesley Ivan Hurt_, Jun 08 2016: (Start)

%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

%F a(n) = (21*n-15-12*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.

%F a(3k) = 7k-3, a(3k-1) = 7k-4, a(3k-2) = 7k-5. (End)

%p seq(7*floor(n/3)+(n mod 3)+2, n= 0..52); # _Gary Detlefs_, Mar 09 2010

%t Select[Range[0, 150], MemberQ[{2, 3, 4}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Jun 08 2016 *)

%o (Magma) [n : n in [0..150] | n mod 7 in [2..4]]; // _Wesley Ivan Hurt_, Jun 08 2016

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_