A240816 -id:A240816 - cp's OEIS frontend

A240813 Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = length (or lifetime) of the meta-Fibonacci sequence f(1) = ... = f(n) = 1; 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, 14, 164, 54, 13, 0, 0, 10, 11, 60, 37, 11, 12, 13, 2354, 30, 13, 13, 14, 15, 282, 63, 44, 14, 15, 17, 18, 1336, 368, 31, 15, 17, 18, 19, 20, 100, 47, 49, 17, 18, 19, 20, 21, 22, 1254, 46, 38, 18, 19, 20, 21, 22, 23, 24, 366, 108, 80, 19, 20, 21, 22, 23

Offset: 1

N. J. A. Sloane, Apr 15 2014

The zero entries (except T(4,1)) are only conjectural.

			Triangle begins:
6,
0, 14,
164, 54, 13,
0, 0, 10, 11,
60, 37, 11, 12, 13,
2354, 30, 13, 13, 14, 15,
282, 63, 44, 14, 15, 17, 18,
1336, 368, 31, 15, 17, 18, 19
...

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 A134680, A240811, A240812.

See A240816 for another version.

More terms from Lars Blomberg, Oct 24 2014

A240810 a(n) = index of first nonexisting term of the meta-Fibonacci sequence {f(1) = ... = f(n) = 1; 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, 165, 0, 61, 2355, 283, 1337, 101, 1255, 367, 420, 499, 484, 779, 1205, 293, 374, 846, 839, 1119, 2121, 816, 2617, 687, 1196, 746, 1113, 2133, 1589, 755, 1228, 1280, 1662, 717, 2276, 785, 2342, 1875, 1464, 1123, 2801, 1351, 1614, 2280, 1558, 1533

Offset: 1

N. J. A. Sloane, Apr 15 2014

nonn

a(2)=0 is only a conjecture (see A005185), whereas a(4)=0 is a theorem of Balamohan et al. (2007).

Except for the two zero entries, this is equal to A134680(n)+1. See that entry for further information.

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 A134680 for another version.

A diagonal of the triangle in A240816.

A240814 a(n) = index of first nonexisting term of the meta-Fibonacci sequence {f(1) = ... = f(n) = 1; 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

15, 55, 0, 38, 31, 64, 369, 48, 47, 109, 189, 119, 63, 210

Offset: 2

N. J. A. Sloane, Apr 15 2014

a(4)=0 is only a conjecture.

Except for the zero entry, this is equal to A240811(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 A240811 for another version.

A diagonal of the triangle in A240816.

A240815 a(n) = index of first nonexisting term of the meta-Fibonacci sequence {f(1) = ... = f(n) = 1; 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

14, 11, 12, 14, 45, 32, 50, 39, 81, 59, 70, 62, 58

Offset: 3

N. J. A. Sloane, Apr 15 2014

This is equal to A240812(n)+1. See that entry for further information.

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 A240812 for another version.

A diagonal of the triangle in A240816.

cp's OEIS Frontend

A240813 Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = length (or lifetime) of the meta-Fibonacci sequence f(1) = ... = f(n) = 1; 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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A240810 a(n) = index of first nonexisting term of the meta-Fibonacci sequence {f(1) = ... = f(n) = 1; 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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A240814 a(n) = index of first nonexisting term of the meta-Fibonacci sequence {f(1) = ... = f(n) = 1; 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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A240815 a(n) = index of first nonexisting term of the meta-Fibonacci sequence {f(1) = ... = f(n) = 1; 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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