A134680 -id:A134680 - 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.

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

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

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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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.

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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