cp's OEIS Frontend

A309567 a(1) = 4, a(2) = 2, a(3) = 5, a(4) = 3, a(5) = 1; a(n) = a(n-a(n-1)) + a(n-a(n-4)) for n > 5.

%I A309567 #26 May 09 2020 00:45:00
%S A309567 4,2,5,3,1,4,7,5,8,6,4,12,5,13,6,9,17,5,18,6,9,22,5,23,11,9,27,5,28,
%T A309567 11,9,32,5,33,11,14,37,5,38,11,14,42,5,43,11,14,47,5,48,16,14,52,5,53,
%U A309567 16,14,57,5,58,16,14,62,5,63,16,19,67,5,68,16,19,72,5,73,16,19,77,5,78,16,19,82,5,83,21,19,87,5
%N A309567 a(1) = 4, a(2) = 2, a(3) = 5, a(4) = 3, a(5) = 1; a(n) = a(n-a(n-1)) + a(n-a(n-4)) for n > 5.
%C A309567 A well-defined quasi-periodic solution for Hofstadter V recurrence (a(n) = a(n-a(n-1)) + a(n-a(n-4))).
%H A309567 Robert Israel, <a href="/A309567/b309567.txt">Table of n, a(n) for n = 1..10000</a>
%H A309567 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 A309567 For k >= 1:
%F A309567 a(5*k)   = 5*floor(sqrt(k-1))+1,
%F A309567 a(5*k+1) = 5*round(sqrt(k))-1,
%F A309567 a(5*k+2) = 5*k+2,
%F A309567 a(5*k+3) = 5,
%F A309567 a(5*k+4) = 5*k+3.
%p A309567 f:= proc(n) local k,j;
%p A309567   j:= n mod 5;
%p A309567   k:= (n-j)/5;
%p A309567   if j=0 then 5*floor(sqrt(k-1))+1
%p A309567   elif j=1 then 5*round(sqrt(k))-1
%p A309567   elif j=2 then 5*k+2
%p A309567   elif j=3 then 5
%p A309567   else 5*k+3
%p A309567   fi
%p A309567 end proc:
%p A309567 f(1):= 4:
%p A309567 map(f, [$1..100]); # _Robert Israel_, Aug 08 2019
%t A309567 a[n_] := a[n] = If[n < 6, {4, 2, 5, 3, 1}[[n]], a[n - a[n-1]] + a[n - a[n-4]]]; Array[a, 88] (* _Giovanni Resta_, Aug 08 2019 *)
%o A309567 (PARI) q=vector(100); q[1]=4; q[2]=2; q[3]=5; q[4]=3; q[5]=1; for(n=6, #q, q[n]=q[n-q[n-1]]+q[n-q[n-4]]); q
%Y A309567 Cf. A063882, A244477, A296518, A309492, A309494, A309496, A309554.
%K A309567 nonn,easy
%O A309567 1,1
%A A309567 _Altug Alkan_ and _Rémy Sigrist_, Aug 08 2019