

A240825


Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = index of first nonexisting term of the metaFibonacci sequence {f(i)=i for i <= n; thereafter 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.


4



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
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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 nonpatterns in a family of metaFibonacci 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 nonpatterns in a family of metaFibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014; Part 1, Part 2.
Index entries for Hofstadtertype 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



