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Numbers that are congruent to {0, 4, 5} mod 7.
1

%I #14 Sep 08 2022 08:44:57

%S 0,4,5,7,11,12,14,18,19,21,25,26,28,32,33,35,39,40,42,46,47,49,53,54,

%T 56,60,61,63,67,68,70,74,75,77,81,82,84,88,89,91,95,96,98,102,103,105,

%U 109,110,112,116,117,119,123,124,126,130,131,133,137,138,140

%N Numbers that are congruent to {0, 4, 5} mod 7.

%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*(4+x+2*x^2) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 04 2011

%F From _Wesley Ivan Hurt_, Jun 09 2016: (Start)

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

%F a(n) = (21*n-15-3*cos(2*n*Pi/3)-5*sqrt(3)*sin(2*n*Pi/3))/9.

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

%p A047375:=n->(21*n-15-3*cos(2*n*Pi/3)-5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047375(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016

%t Select[Range[0, 150], MemberQ[{0, 4, 5}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)

%o (Magma) [n : n in [0..150] | n mod 7 in [0, 4, 5]]; // _Wesley Ivan Hurt_, Jun 09 2016

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_