A240822 -id:A240822 - cp's OEIS frontend

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

N. J. A. Sloane, Apr 15 2014

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.

			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, ...
  ...

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.

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

Diagonals give A240822, A240823, A240824.

See A240821 for another version.

A240818 a(n) = length (or lifetime) of the meta-Fibonacci sequence f(k) = k for k <= n; f(k)=f(k-f(k-1))+f(k-f(k-n)) if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite.

Original entry on oeis.org

6, 0, 162, 0, 56, 2349, 276, 1300, 84, 1245, 356, 408, 486, 470, 764, 1172, 258, 356, 805, 819, 1078, 2099, 470, 2593, 662, 1170, 665, 1085, 2104, 1417, 724, 1196, 1247, 1628, 648, 2240, 712, 2304, 1836, 1424, 1082, 2759, 1264, 1570, 2235, 1512, 1442, 2447

Offset: 1

N. J. A. Sloane, Apr 15 2014

nonn

The terms a(2) = 0 and a(4) = 0 are only conjectural.

This sequence is very similar to A134680.

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.

Lars Blomberg, Table of n, a(n) for n = 1..10000, "infinity" = 10^8.
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

The sequences for n=2,3,4 are A005185 and (essentially) A046700, A063882.
See A240822 for another version.
A diagonal of the triangle in A240821.
Cf. A134680.

More terms from Lars Blomberg, Oct 24 2014

cp's OEIS Frontend

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.

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