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%I #28 Sep 08 2022 08:44:51
%S 1,2,3,5,6,8,9,10,12,13,15,16,17,19,20,22,23,24,26,27,29,30,31,33,34,
%T 36,37,38,40,41,43,44,45,47,48,50,51,52,54,55,57,58,59,61,62,64,65,66,
%U 68,69,71,72,73,75,76,78,79,80,82,83,85,86,87,89,90,92,93,94,96,97,99
%N Numbers that are congruent to {1, 2, 3, 5, 6} mod 7.
%C If k is a term, then k*(k+1)*(k+2)*...*(k+6)/(k+(k+1)+(k+2)+...+(k+6)) is a multiple of k.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).
%F Equals natural numbers minus '4, 7, 11, 14, 18, ...' (= previous term +3, +4, +3, +4, ...).
%F G.f.: x*(x^5 + x^4 + 2*x^3 + x^2 + x + 1)/((1-x)*(1-x^5)).
%F a(n) = (m^3 - 6*m^2 + 17*m + 6*(7*floor(n/5)-1))/6, where m = n mod 5. - _Luce ETIENNE_,Oct 17 2018
%t #+{1,2,3,5,6}&/@(7*Range[0,15])//Flatten (* or *) LinearRecurrence[ {1,0,0,0,1,-1},{1,2,3,5,6,8},100] (* _Harvey P. Dale_, Oct 07 2018 *)
%o (Magma) [n: n in [0..120] | n mod 7 in {1, 2, 3, 5, 6}]; // _Vincenzo Librandi_, Dec 29 2010
%Y Cf. A032765..A032798.
%Y Cf. A010874.
%K nonn,easy
%O 1,2
%A _Patrick De Geest_, May 15 1998