%I #21 Sep 08 2022 08:45:09
%S 3,7,7,11,15,19,19,23,27,31,31,35,39,43,43,47,51,55,55,59,63,67,67,71,
%T 75,79,79,83,87,91,91,95,99,103,103,107,111,115,115,119,123,127,127,
%U 131,135,139,139,143,147,151,151,155,159,163,163,167,171,175
%N a(1)=3; for n>1, a(n)=a(n-1) if n is already in the sequence, a(n)=a(n-1)+4 otherwise.
%H B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
%H B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://arXiv.org/abs/math.NT/0305308">Numerical analogues of Aronson's sequence</a> (math.NT/0305308)
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F a(n) = 3 + 4*(n-2-floor((n-3)/4)).
%F From _Wesley Ivan Hurt_, Jul 15 2015: (Start)
%F G.f.: x*(3+4*x+4*x^3+x^4)/((x-1)^2*(1+x+x^2+x^3)).
%F a(n) = a(n-1)+a(n-4)-a(n-5), n>5.
%F a(n) = (6*n-1+(-1)^n-2*(-1)^((2*n+1-(-1)^n)/4))/2. (End)
%p A080457:=n->3+4*(n-2-floor((n-3)/4)): seq(A080457(n), n=1..100); # _Wesley Ivan Hurt_, Jul 15 2015
%t CoefficientList[Series[(3 + 4 x + 4 x^3 + x^4)/((x - 1)^2*(1 + x + x^2 + x^3)), {x, 0, 100}], x] (* _Wesley Ivan Hurt_, Jul 15 2015 *)
%t LinearRecurrence[{1, 0, 0, 1, -1}, {3, 7, 7, 11, 15}, 70] (* _Vincenzo Librandi_, Jul 16 2015 *)
%o (Magma) [3+4*(n-2-Floor((n-3)/4)) : n in [1..100]]; // _Wesley Ivan Hurt_, Jul 15 2015
%o (PARI) main(size)={my(v=vector(size),i,j);v[1]=3;for(j=2,size,x=0;for(i=1,j-1,if(v[i]==j,x=1;break));if(x==1,v[j]=v[j-1],v[j]=v[j-1]+4));return(v);} /* _Anders Hellström_, Jul 15 2015 */
%Y Cf. A080036, A080037, A080455, A080456, A080457, A080458.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_ and _Benoit Cloitre_, Mar 20 2003