Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #21 May 08 2017 21:07:45
%S 1,2,2,2,3,4,5,5,5,5,6,8,10,10,10,9,10,10,10,10,11,13,18,20,18,15,15,
%T 15,20,20,19,18,20,20,20,19,20,20,20,20,21,23,31,38,33,28,20,20,21,30,
%U 39,39,38,30,29,25,35,40,40,38,31,33,36,40,38,40,35,40,40,40,39,38,40,40,40,39,40,40,40,40,41,43,54,69
%N a(1) = 1; a(2) = a(3) = a(4) = 2; a(n) = a(a(n-1)-1) + a(n-a(n-3)) for n > 4.
%C Although sequence is unpredictable with its complex growth characteristic and generational structure, it has various signs of order and there are many temporary and simple patterns on it. For example, values of a(n) such that a(n) = a(n + 1) = a(n + 2) = a(n + 3) are 5, 10, 20, 40, 80, 160, 320, 640, 1280, ...
%H Altug Alkan, <a href="/A285509/b285509.txt">Table of n, a(n) for n = 1..10000</a>
%H Altug Alkan, <a href="/A285509/a285509.png">Alternative scatterplot of A285509</a>
%e a(5) = 3 because a(5) = a(a(4)-1) + a(5-a(2)) = a(1) + a(3) = 2.
%t a[1]=1; a[2]=a[3]=a[4]=2; a[n_] := a[n] = a[a[n-1]-1] + a[n-a[n-3]]; Array[a, 84] (* _Giovanni Resta_, Apr 21 2017 *)
%o (PARI) a=vector(10000); a[1]=1;a[2]=a[3]=a[4]=2; for(n=5, #a, a[n]=a[a[n-1]-1]+a[n-a[n-3]]); va = vector(10000, n, a[n])
%Y Cf. A005185, A055748, A284523, A285507
%K nonn,look
%O 1,2
%A _Altug Alkan_, Apr 20 2017