A240818 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.

6, 0, 162, 0, 56, 2349, 276, 1300, 84, 1245, 356, 408, 486, 470, 764, 1172, 258, 356, 805, 819, 1078, 2099, 470, 2593, 662, 1170, 665, 1085, 2104, 1417, 724, 1196, 1247, 1628, 648, 2240, 712, 2304, 1836, 1424, 1082, 2759, 1264, 1570, 2235, 1512, 1442, 2447

Offset: 1

Author

N. J. A. Sloane, Apr 15 2014

Keywords

• nonn

Comments

The terms a(2) = 0 and a(4) = 0 are only conjectural.

This sequence is very similar to A134680.

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 = 1..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

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

See A240822 for another version.

A diagonal of the triangle in A240821.

Cf. A134680.

Extensions

More terms from Lars Blomberg, Oct 24 2014