cp's OEIS Frontend

A309704 a(1) = 3, a(2) = 4, a(3) = 5, a(4) = 4, a(5) = 5; a(6) = 6; a(n) = a(n-a(n-1)) + a(n-a(n-4)) for n > 6.

%I A309704 #29 May 09 2020 00:45:28
%S A309704 3,4,5,4,5,6,7,7,8,8,9,10,10,10,11,11,13,12,14,14,14,15,15,16,17,17,
%T A309704 18,18,19,19,20,20,20,21,21,22,24,23,23,25,24,26,27,27,26,28,28,28,29,
%U A309704 29,30,31,31,32,32,33,33,34,35,35,35,36,36,37,37,38,39,39,39,40,40,40,41,41,42,43,43,45,45,45,45,48,44,48,49,47,52,47,51,50,47,52,50,54,52,54,55,54,54,56
%N A309704 a(1) = 3, a(2) = 4, a(3) = 5, a(4) = 4, a(5) = 5; a(6) = 6; a(n) = a(n-a(n-1)) + a(n-a(n-4)) for n > 6.
%C A309704 This sequence is finite but has an exceptionally long life: a(3080193026) = 3101399868 is its last term since a(3080193027) refers to a nonpositive index and thus fails to exist. See plots in Links section to fractal-like structure of a(n)-n/2.
%H A309704 Altug Alkan, <a href="/A309704/b309704.txt">Table of n, a(n) for n = 1..20000</a>
%H A309704 Altug Alkan, Nathan Fox, Orhan Ozgur Aybar, Zehra Akdeniz, <a href="https://arxiv.org/abs/2002.03396">On Some Solutions to Hofstadter's V-Recurrence</a>, arXiv:2002.03396 [math.DS], 2020.
%H A309704 Rémy Sigrist, <a href="/A309704/a309704.png">Density plot of a(n)-n/2 for n <= 10^8</a>
%H A309704 Rémy Sigrist, <a href="/A309704/a309704_1.png">Scatterplot of a(n)-n/2 for n <= 10^8</a>
%H A309704 Rémy Sigrist, <a href="/A309704/a309704_2.png">Density plot of the whole sequence (n = 1..3080193026)</a>
%t A309704 Nest[Append[#, #[[-#[[-1]] ]] + #[[-#[[-4]] ]]] &, {3, 4, 5, 4, 5, 6}, 94] (* _Michael De Vlieger_, May 08 2020 *)
%o A309704 (PARI) q=vector(100); q[1]=3; q[2]=4; q[3]=5; q[4]=4; q[5]=5; q[6]=6; for(n=7, #q, q[n] = q[n-q[n-1]] + q[n-q[n-4]]); q
%Y A309704 Cf. A005185, A063882, A309567, A309636.
%K A309704 nonn,look,fini
%O A309704 1,1
%A A309704 _Altug Alkan_ and _Rémy Sigrist_, Aug 13 2019
%E A309704 a(3080193026) from _Giovanni Resta_, Aug 13 2019