A240820 a(n) = length (or lifetime) of the meta-Fibonacci sequence f(k) = k for k <= n; f(k) = f(k-f(k-3)) + f(k-f(k-n)) if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite.

20, 71, 34, 0, 46, 34, 36, 39, 90, 0, 142, 70, 91, 94, 255, 2004, 306, 525, 259, 454, 304, 1866, 316, 198, 254, 297, 415, 3315, 348, 406, 397, 420, 903, 1226, 408, 589, 1294, 535, 490, 958, 1343, 477, 492, 915, 1378, 1723, 797, 1869, 745, 696, 863, 1070, 560

Offset: 3

Author

N. J. A. Sloane, Apr 15 2014

Keywords

• nonn

Comments

The term a(6) = 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 = 3..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.
• Index entries for Hofstadter-type sequences

Crossrefs

See A240827 for the sequence for n=6.

See A240823 for another version.

A diagonal of the triangle in A240821.

Extensions

More terms from Lars Blomberg, Oct 24 2014