cp's OEIS Frontend

A080033 a(n) is taken to be the smallest positive integer not already present which is consistent with the condition "n is a member of the sequence if and only if a(n) is a multiple of 4".

%I A080033 #10 Sep 27 2016 21:09:07
%S A080033 0,2,4,5,8,12,7,16,20,10,24,13,28,32,15,36,40,18,44,21,48,52,23,56,60,
%T A080033 26,64,29,68,72,31,76,80,34,84,37,88,92,39,96,100,42,104,45,108,112,
%U A080033 47,116,120,50,124,53,128,132,55,136,140,58,144,61,148,152,63,156,160,66
%N A080033 a(n) is taken to be the smallest positive integer not already present which is consistent with the condition "n is a member of the sequence if and only if a(n) is a multiple of 4".
%H A080033 B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
%H A080033 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)
%F A080033 a(8m)=20m, a(8m+1)=8m+2, a(8m+2)=20m+4, a(8m+3)=8m+5, a(8m+4)=20m+8, a(8m+5)=20m+12, a(8m+6)=8m+7, a(8m+7)=20m+16.
%F A080033 From _Chai Wah Wu_, Sep 27 2016: (Start)
%F A080033 a(n) = 2*a(n-8) - a(n-16) for n > 15.
%F A080033 G.f.: x*(4*x^14 + x^13 + 8*x^12 + 12*x^11 + 3*x^10 + 16*x^9 + 6*x^8 + 20*x^7 + 16*x^6 + 7*x^5 + 12*x^4 + 8*x^3 + 5*x^2 + 4*x + 2)/(x^16 - 2*x^8 + 1). (End)
%Y A080033 Cf. A079000, A080030, A080032, A079313, A080034.
%K A080033 easy,nonn
%O A080033 0,2
%A A080033 _N. J. A. Sloane_, Mar 14 2003
%E A080033 More terms from _Matthew Vandermast_, Mar 23 2003