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%I #8 Jul 31 2015 22:33:24
%S 4,14,22,25,35,55,69,74,90,120,140,147,169,209,235,244,272,322,354,
%T 365,399,459,497,510,550,620,664,679,725,805,855,872,924,1014,1070,
%U 1089,1147,1247,1309,1330,1394,1504,1572,1595,1665,1785,1859,1884,1960,2090
%N Integers of the form k*(k+13)/12.
%C Integers of the form k+k*(k+1)/12 = k+A000217(k)/6 (see A069497). - R. J. Mathar, Sep 25 2009
%C Are all terms composite numbers?
%C Contribution from _Zak Seidov_, Sep 25 2009: (Start)
%C Integers of form n(13+n)/12, n=0,1,2,...
%C Each four terms of the sequence are composite numbers of forms:
%C {(4+3 m) (1+4 m), (2+3 m) (7+4 m), (2+m) (11+12 m), m (13+12 m)}, m=0,1,2,...
%C m=0: {4,14,22,25}; m=1: {35,55,69,74}; m=2: {90,120,140,147}, etc. (End)
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3, -5, 7, -7, 5, -3, 1).
%F a(n)= 3*a(n-1) -5*a(n-2) +7*a(n-3) -7*a(n-4) +5*a(n-5) -3*a(n-6) +a(n-7). - R. J. Mathar, Sep 25 2009
%F G.f.: x*(-4-2*x-x^3+x^5)/((x^2+1)^2*(x-1)^3). - R. J. Mathar, Sep 25 2009
%t q=6;s=0;lst={};Do[s+=((n+q)/q);If[IntegerQ[s],AppendTo[lst,s]],{n,6!}];lst
%t Select[Table[k (k+13)/12,{k,200}],IntegerQ] (* or *) LinearRecurrence[ {3,-5,7,-7,5,-3,1},{4,14,22,25,35,55,69},50] (* _Harvey P. Dale_, Jan 30 2013 *)
%Y Cf. A165717, A165718, A165719, A165720.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Sep 24 2009
%E Definition simplified by _R. J. Mathar_, Sep 25 2009
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