A240811 a(n) = length (or lifetime) of the meta-Fibonacci sequence f(1) = ... = f(n) = 1; 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.

14, 54, 0, 37, 30, 63, 368, 47, 46, 108, 188, 118, 62, 209, 126, 197, 78, 127, 190, 141, 94, 130, 138, 226, 110, 134, 158, 138, 126, 170, 242, 371, 142, 190, 178, 225, 158, 206, 214, 304, 174, 226, 238, 245, 190, 250, 262, 328, 206, 234, 278, 357, 222, 290

Offset: 2

Author

N. J. A. Sloane, Apr 15 2014

Keywords

• nonn

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 100 terms
• Index entries for Hofstadter-type sequences

Crossrefs

Cf. A063892, A087777, A240817 (sequences for n=3..5).

See A240814 for another version.

A diagonal of the triangle in A240813.

Extensions

More terms from Lars Blomberg, Oct 24 2014