A240809 - OEIS

%I #24 Sep 08 2022 08:46:07

%S 1,2,3,4,6,6,5,6,7,8,10,10,9,10,12,12,12,12,10,12,17,16,15,16,14,16,

%T 19,20,20,18,20,20,18,22,24,22,19,24,24,24,28,24,22,24,27,32,26,28,31,

%U 28,26,32,35,32,32,32,30,32,39,40,36,34,35,34,38,40,40,42,40,38,40,40,36,44,48,42,48,44,40,46,46,46,41,48,48,48,56,48,46,48,51,48

%N a(n) = n for 1 <= n <= 4; thereafter a(n) = a(n - a(n-2)) + a(n - a(n-4)).

%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="/A240809/b240809.txt">Table of n, a(n) for n = 1..20000</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 D. R. Hofstadter, <a href="/A240809/a240809.pdf">Plot of first 100000 terms</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:=2; s:=4;

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

%o (Magma) I:=[1, 2, 3, 4]; [n le 4 select I[n] else Self(n-Self(n-2))+Self(n-Self(n-4)): n in [1..100]]; // _Vincenzo Librandi_, Apr 16 2014

%Y Cf. A240821.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Apr 15 2014, Apr 17 2014