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A240819 a(n) = length (or lifetime) of the meta-Fibonacci sequence f(k) = k for k <= n; f(k)=f(k-f(k-2))+f(k-f(k-n)) if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite. 3

%I #17 Oct 25 2014 01:27:44

%S 13,29,0,29,24,50,0,332,56,848,2936,140,370,605,1514,532,169,360,1784,

%T 514,713,279,817,945,973,949,932,444,1529,420,2345,628,517,913,713,

%U 738,1611,1066,1639,727,1256,1140,1336,718,941,907,2272,606,1152,2091,2341

%N a(n) = length (or lifetime) of the meta-Fibonacci sequence f(k) = k for k <= n; f(k)=f(k-f(k-2))+f(k-f(k-n)) if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite.

%C The term a(4) = 0 is only conjectural.

%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 Lars Blomberg, <a href="/A240819/b240819.txt">Table of n, a(n) for n = 2..10000</a>, "infinity" = 10^8.

%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="/A240819/a240819.pdf">Graph of first 30000 terms</a>

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

%Y See A240809 for the sequence for n=4.

%Y See A240823 for another version.

%Y A diagonal of the triangle in A240821.

%K nonn

%O 2,1

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

%E More terms from _Lars Blomberg_, Oct 24 2014

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Last modified April 24 18:05 EDT 2024. Contains 371962 sequences. (Running on oeis4.)