login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

a(n) = length (or lifetime) of the meta-Fibonacci sequence f(k) = k for k <= n; 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.
3

%I #16 May 22 2019 14:21:11

%S 6,0,162,0,56,2349,276,1300,84,1245,356,408,486,470,764,1172,258,356,

%T 805,819,1078,2099,470,2593,662,1170,665,1085,2104,1417,724,1196,1247,

%U 1628,648,2240,712,2304,1836,1424,1082,2759,1264,1570,2235,1512,1442,2447

%N a(n) = length (or lifetime) of the meta-Fibonacci sequence f(k) = k for k <= n; 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 The terms a(2) = 0 and a(4) = 0 are only conjectural.

%C This sequence is very similar to A134680.

%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="/A240818/b240818.txt">Table of n, a(n) for n = 1..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 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

%Y The sequences for n=2,3,4 are A005185 and (essentially) A046700, A063882.

%Y See A240822 for another version.

%Y A diagonal of the triangle in A240821.

%Y Cf. A134680.

%K nonn

%O 1,1

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

%E More terms from _Lars Blomberg_, Oct 24 2014