A240825 -id:A240825 - cp's OEIS frontend

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.

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

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.

			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, ...
...

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.
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

Diagonals give A240818, A240819, A240820.

See A240825 for another version.

More terms from Lars Blomberg, Oct 24 2014

A240823 a(n) = index of first nonexisting term of the meta-Fibonacci sequence {f(k) = k for k <= n; f(k)=f(k-f(k-2))+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

14, 30, 0, 30, 25, 51, 0, 333, 57, 849, 2937, 141, 371, 606

Offset: 2

N. J. A. Sloane, Apr 15 2014

a(4)=0 and a(8)=0 are only conjectures.

Except for the zero entries, this is equal to A240819(n)+1. See that entry for further information.

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

See A240819 for another version.

A diagonal of the triangle in A240825.

A240822 a(n) = index of first nonexisting term 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

7, 0, 163, 0, 57, 2350, 277, 1301, 85, 1246, 357, 409, 487, 471, 765, 1173, 259, 357, 806, 820, 1079, 2100, 471, 2594, 663, 1171, 666, 1086, 2105, 1418, 725, 1197, 1248, 1629, 649, 2241, 713, 2305, 1837, 1425, 1083, 2760, 1265, 1571, 2236, 1513, 1443, 2448

Offset: 1

N. J. A. Sloane, Apr 15 2014

nonn

a(2)=0 and a(4)=0 are conjectural.
Except for the two zero entries, this is equal to A240818(n)+1. See that entry for further information.
Similar to A134680 and A240810.

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

See A240818 for another version.
A diagonal of the triangle in A240825.
Cf. A134680, A240810.

More terms from Max Alekseyev, Sep 19 2023

A240824 a(n) = index of first nonexisting term of the meta-Fibonacci sequence {f(k) = k for k <= n; f(k)=f(k-f(k-3))+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

21, 72, 35, 0, 47, 35, 37, 40, 91, 0, 143, 71, 92

Offset: 3

N. J. A. Sloane, Apr 15 2014

a(6)=0 and a(12)=0 are only conjectures.

Except for the zero entries, this is equal to A240820(n)+1. See that entry for further information.

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

See A240820 for another version.

A diagonal of the triangle in A240825.

cp's OEIS Frontend

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.

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A240823 a(n) = index of first nonexisting term of the meta-Fibonacci sequence {f(k) = k for k <= n; f(k)=f(k-f(k-2))+f(k-f(k-n))} if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite.

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A240822 a(n) = index of first nonexisting term 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.

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Extensions

A240824 a(n) = index of first nonexisting term of the meta-Fibonacci sequence {f(k) = k for k <= n; f(k)=f(k-f(k-3))+f(k-f(k-n))} if that sequence is only defined for finitely many terms, or 0 if that sequence is infinite.

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