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

1,1

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.

Sequence in context: A246137 A052679 A266218 * A134680 A362794 A336303

Adjacent sequences: A240815 A240816 A240817 * A240819 A240820 A240821

Keyword

nonn

Author

N. J. A. Sloane, Apr 15 2014

Extensions

More terms from Lars Blomberg, Oct 24 2014

Status

approved