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A309650 a(1) = 3, a(2) = 1, a(3) = 4, a(4) = 2; a(n) = a(n-a(n-2)) + a(n-a(n-3)) for n > 4.

%I A309650 #17 Sep 08 2022 08:46:21
%S A309650 3,1,4,2,5,3,6,9,7,5,3,11,14,7,5,8,16,19,7,5,8,21,24,12,5,8,26,29,12,
%T A309650 5,8,31,34,12,5,13,36,39,12,5,13,41,44,12,5,13,46,49,17,5,13,51,54,17,
%U A309650 5,13,56,59,17,5,13,61,64,17,5,18,66,69,17,5,18,71,74,17,5,18,76,79,17,5,18,81,84,22,5
%N A309650 a(1) = 3, a(2) = 1, a(3) = 4, a(4) = 2; a(n) = a(n-a(n-2)) + a(n-a(n-3)) for n > 4.
%C A309650 A well-defined quasi-periodic solution for recurrence (a(n) = a(n-a(n-2)) + a(n-a(n-3))).
%H A309650 Michael De Vlieger, <a href="/A309650/b309650.txt">Table of n, a(n) for n = 1..10000</a>
%H A309650 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.
%F A309650 For k >= 1:
%F A309650 a(5*k)   = 5,
%F A309650 a(5*k+1) = 5*floor(sqrt(k)+1/2)-2,
%F A309650 a(5*k+2) = 5*k+1,
%F A309650 a(5*k+3) = 5*k+4,
%F A309650 a(5*k+4) = 5*floor(sqrt(k))+2.
%t A309650 Nest[Append[#, #[[-#[[-2]] ]] + #[[-#[[-3]] ]]] &, {3, 1, 4, 2}, 81] (* _Michael De Vlieger_, May 08 2020 *)
%o A309650 (PARI) q=vector(100); q[1]=3; q[2]=1; q[3]=4; q[4]=2; for(n=5, #q, q[n] = q[n-q[n-2]] + q[n-q[n-3]]); q
%o A309650 (Magma) I:=[3,1,4,2]; [n le 4 select I[n] else  Self(n-Self(n-2)) + Self(n-Self(n-3)): n in [1..90]]; // _Marius A. Burtea_, Aug 11 2019
%Y A309650 Cf. A063892, A244477, A309492, A309567.
%K A309650 nonn,easy
%O A309650 1,1
%A A309650 _Altug Alkan_ and _Nathan Fox_, Aug 11 2019