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

Author

N. J. A. Sloane, Apr 15 2014

Keywords

• nonn
• tabl
• more

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.

Examples

			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, ...
  ...
		

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

• 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

Diagonals give A240822, A240823, A240824.

See A240821 for another version.