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A240827 a(n) = n for 1<=n<=6; thereafter a(n) = a(n-a(n-3))+a(n-a(n-6)).

%I A240827 #26 Sep 08 2022 08:46:07
%S A240827 1,2,3,4,5,6,9,9,9,7,8,9,10,11,12,15,15,15,13,14,15,18,18,18,18,18,18,
%T A240827 14,16,18,25,26,24,23,22,24,20,24,24,29,28,30,29,29,27,30,28,30,27,33,
%U A240827 33,36,32,33,27,36,36,43,36,36,38,36,36,33,32,36,39,50,48,45,39,42,37,40,42,49,44,48,48,53,48,47,42,48,44,53,48,57,52,60
%N A240827 a(n) = n for 1<=n<=6; thereafter a(n) = a(n-a(n-3))+a(n-a(n-6)).
%C A240827 Conjectured to be infinite.
%D A240827 D. R. Hofstadter, Curious patterns and non-patterns in a family of meta-Fibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014.
%H A240827 N. J. A. Sloane, <a href="/A240827/b240827.txt">Table of n, a(n) for n = 1..50000</a>
%H A240827 D. R. Hofstadter, Curious patterns and non-patterns in a family of meta-Fibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014; <a href="https://vimeo.com/91708646">Part 1</a>, <a href="https://vimeo.com/91710600">Part 2</a>.
%H A240827 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%p A240827 #Q(r,s) with initial values 1,2,3,4,...
%p A240827 r:=3; s:=6;
%p A240827 a:=proc(n) option remember; global r,s;
%p A240827 if n <= s then n
%p A240827 else
%p A240827 if (a(n-r) <= n) and (a(n-s) <= n) then
%p A240827 a(n-a(n-r))+a(n-a(n-s));
%p A240827 else lprint("died with n =",n); return (-1);
%p A240827 fi;
%p A240827 fi; end;
%p A240827 t2:=[seq(a(n),n=1..100)];
%t A240827 {a[1]=1,a[2]=2,a[3]=3,a[4]=4,a[5]=5,a[6]=6,a[n_]:=a[n]=a[n-a[n-3]]+ a[n-a[n-6]]};Table[a[x],{x,100}] (* _Harvey P. Dale_, Nov 18 2021 *)
%o A240827 (Magma) I:=[1,2,3,4,5,6]; [n le 6 select I[n] else Self(n-Self(n-3))+Self(n-Self(n-6)): n in [1..100]]; // _Vincenzo Librandi_, Apr 16 2014
%Y A240827 Cf. A240821.
%K A240827 nonn,hear
%O A240827 1,2
%A A240827 _N. J. A. Sloane_, Apr 15 2014