

A240821


Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = length (or lifetime) of the metaFibonacci sequence {f(i) = i for i <= n; f(i)=f(if(ik))+f(if(in))} if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite.


7



6, 0, 13, 162, 29, 20, 0, 0, 71, 27, 56, 29, 34, 35, 28, 2349, 24, 0, 28, 54, 41, 276, 50, 46, 44, 34, 55, 40, 1300, 0, 34, 0, 37, 68, 89, 44, 84, 332, 36, 60, 56, 43, 80, 93, 54, 1245, 56, 39, 44, 0, 48, 48, 71, 87, 57, 356, 848, 90, 46, 74, 68, 51, 55, 227
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



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.


REFERENCES

D. R. Hofstadter, Curious patterns and nonpatterns in a family of metaFibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014.


LINKS

D. R. Hofstadter, Curious patterns and nonpatterns in a family of metaFibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014; Part 1, Part 2.


EXAMPLE

Triangle begins:
6,
0, 13,
162, 29, 20,
0, 0, 71, 27,
56, 29, 34, 35, 28,
2349, 24, 0, 28, 54, 41,
276, 50, 46, 44, 34, 55, 40,
1300, 0, 34, 0, 37, 68, 89, ...
...


CROSSREFS



KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



