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Numbers that are congruent to {0, 2, 3} mod 7.
1

%I #16 Sep 08 2022 08:44:57

%S 0,2,3,7,9,10,14,16,17,21,23,24,28,30,31,35,37,38,42,44,45,49,51,52,

%T 56,58,59,63,65,66,70,72,73,77,79,80,84,86,87,91,93,94,98,100,101,105,

%U 107,108,112,114,115,119,121,122,126,128,129,133,135,136,140

%N Numbers that are congruent to {0, 2, 3} 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*(2+x+4*x^2) / ((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-27-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.

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

%p A047359:=n->(21*n-27-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047359(n), n=1..100); # _Wesley Ivan Hurt_, Jun 08 2016

%t Select[Range[0,150], MemberQ[{0,2,3}, Mod[#,7]]&] (* _Harvey P. Dale_, Dec 06 2012 *)

%o (Magma) [n : n in [0..150] | n mod 7 in [0, 2, 3]]; // _Wesley Ivan Hurt_, Jun 08 2016

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_