A240825 Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = index of first nonexisting term of the meta-Fibonacci sequence {f(i)=i for i <= n; thereafter f(i)=f(i-f(i-k))+f(i-f(i-n))} if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite.

7, 0, 14, 163, 30, 21, 0, 0, 72, 28, 57, 30, 35, 36, 29, 2350, 25, 0, 29, 55, 42, 277, 51, 47, 45, 35, 56, 41, 1301, 0, 35, 0, 38, 69, 90

Offset

1,1

Comments

The zero entries are only conjectural. More precisely, Hofstadter conjectures that T(n,k) = 0 (i.e., the sequence is immortal) iff n = 2k or n = 4k.

Apart from the zero entries, equals A240821 + 1.

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

Table of n, a(n) for n=1..35.

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

Example

Triangle begins:
     7;
     0, 14;
   163, 30, 21;
     0,  0, 72, 28;
    57, 30, 35, 36, 29;
  2350, 25,  0, 29, 55, 42;
   277, 51, 47, 45, 35, 56, 41;
  1301,  0, 35,  0, 38, 69, 90, ...
  ...

Crossrefs

Diagonals give A240822, A240823, A240824.

See A240821 for another version.

Sequence in context: A169603 A022920 A331423 * A243773 A097604 A240816

Adjacent sequences: A240822 A240823 A240824 * A240826 A240827 A240828

Keyword

nonn,tabl,more

Author

N. J. A. Sloane, Apr 15 2014

Status

approved