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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)). 4

%I

%S 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 14,16,18,25,26,24,23,22,24,20,24,24,29,28,30,29,29,27,30,28,30,27,33,

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

%C Conjectured to be infinite.

%D 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 N. J. A. Sloane, <a href="/A240827/b240827.txt">Table of n, a(n) for n = 1..50000</a>

%H 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 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

%p #Q(r,s) with initial values 1,2,3,4,...

%p r:=3; s:=6;

%p a:=proc(n) option remember; global r,s;

%p if n <= s then n

%p else

%p if (a(n-r) <= n) and (a(n-s) <= n) then

%p a(n-a(n-r))+a(n-a(n-s));

%p else lprint("died with n =",n); return (-1);

%p fi;

%p fi; end;

%p t2:=[seq(a(n),n=1..100)];

%o (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 Cf. A240821.

%K nonn,hear

%O 1,2

%A _N. J. A. Sloane_, Apr 15 2014

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Last modified December 4 21:58 EST 2020. Contains 338941 sequences. (Running on oeis4.)