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Numbers that are congruent to {0, 2, 5} mod 7.
2

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

%S 0,2,5,7,9,12,14,16,19,21,23,26,28,30,33,35,37,40,42,44,47,49,51,54,

%T 56,58,61,63,65,68,70,72,75,77,79,82,84,86,89,91,93,96,98,100,103,105,

%U 107,110,112,114,117,119,121,124,126,128,131,133,135,138,140

%N Numbers that are congruent to {0, 2, 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 a(n+1) = 3*n-2*floor(n/3)-(n^2 mod 3). - _Gary Detlefs_, Mar 19 2010

%F G.f.: x^2*(2+3*x+2*x^2)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 05 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-21+3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.

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

%p seq(3*n-2*floor(n/3)-(n^2 mod 3), n=0..52); # _Gary Detlefs_, Mar 19 2010

%t Select[Range[0, 150], MemberQ[{0, 2, 5}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)

%o (Magma) [n : n in [0..150] | n mod 7 in [0, 2, 5]]; // _Wesley Ivan Hurt_, Jun 09 2016

%Y Cf. A011655. [_Gary Detlefs_, Mar 19 2010]

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_