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A240821 Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = length (or lifetime) of the meta-Fibonacci sequence {f(i) = i for i <= n; 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
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 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.

B. Balamohan, A. Kuznetsov and S. Tanny, On the behavior of a variant of Hofstadter's Q-sequence, J. Integer Sequences, Vol. 10 (2007), #07.7.1.

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:

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

Diagonals give A240818, A240819, A240820.

See A240825 for another version.

Sequence in context: A028603 A205966 A183772 * A320146 A283999 A240813

Adjacent sequences:  A240818 A240819 A240820 * A240822 A240823 A240824

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Apr 15 2014

EXTENSIONS

More terms from Lars Blomberg, Oct 24 2014

STATUS

approved

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Last modified November 24 07:53 EST 2020. Contains 338607 sequences. (Running on oeis4.)