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a(n) = index of first nonexisting term 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 #14 Jul 16 2015 23:02:48

%S 14,30,0,30,25,51,0,333,57,849,2937,141,371,606

%N a(n) = index of first nonexisting term 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 a(4)=0 and a(8)=0 are only conjectures.

%C Except for the zero entries, this is equal to A240819(n)+1. See that entry for further information.

%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 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>

%Y See A240819 for another version.

%Y A diagonal of the triangle in A240825.

%K nonn,more

%O 2,1

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