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.

13, 29, 0, 29, 24, 50, 0, 332, 56, 848, 2936, 140, 370, 605, 1514, 532, 169, 360, 1784, 514, 713, 279, 817, 945, 973, 949, 932, 444, 1529, 420, 2345, 628, 517, 913, 713, 738, 1611, 1066, 1639, 727, 1256, 1140, 1336, 718, 941, 907, 2272, 606, 1152, 2091, 2341

Offset

2,1

Comments

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

References

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.

Links

Lars Blomberg, Table of n, a(n) for n = 2..10000, "infinity" = 10^8.

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; Part 1, Part 2.

D. R. Hofstadter, Graph of first 30000 terms

Index entries for Hofstadter-type sequences

Crossrefs

See A240809 for the sequence for n=4.

See A240823 for another version.

A diagonal of the triangle in A240821.

Sequence in context: A001291 A018974 A018955 * A293661 A087593 A158075

Adjacent sequences: A240816 A240817 A240818 * A240820 A240821 A240822

Keyword

nonn

Author

N. J. A. Sloane, Apr 15 2014

Extensions

More terms from Lars Blomberg, Oct 24 2014

Status

approved