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A240810 a(n) = index of first nonexisting term of the meta-Fibonacci sequence {f(1) = ... = f(n) = 1; f(k)=f(k-f(k-1))+f(k-f(k-n))} if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite.

%I A240810 #21 Jul 16 2015 23:01:54
%S A240810 7,0,165,0,61,2355,283,1337,101,1255,367,420,499,484,779,1205,293,374,
%T A240810 846,839,1119,2121,816,2617,687,1196,746,1113,2133,1589,755,1228,1280,
%U A240810 1662,717,2276,785,2342,1875,1464,1123,2801,1351,1614,2280,1558,1533
%N A240810 a(n) = index of first nonexisting term of the meta-Fibonacci sequence {f(1) = ... = f(n) = 1; f(k)=f(k-f(k-1))+f(k-f(k-n))} if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite.
%C A240810 a(2)=0 is only a conjecture (see A005185), whereas a(4)=0 is a theorem of Balamohan et al. (2007).
%C A240810 Except for the two zero entries, this is equal to A134680(n)+1. See that entry for further information.
%H A240810 B. Balamohan, A. Kuznetsov and S. Tanny, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL10/Tanny/tanny3.html">On the behavior of a variant of Hofstadter's Q-sequence</a>, J. Integer Sequences, Vol. 10 (2007), #07.7.1.
%H A240810 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 A240810 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%Y A240810 See A134680 for another version.
%Y A240810 A diagonal of the triangle in A240816.
%K A240810 nonn
%O A240810 1,1
%A A240810 _N. J. A. Sloane_, Apr 15 2014