A240810 -id:A240810 - cp's OEIS frontend

A134680 a(n) = length (or lifetime) 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.

6, 0, 164, 0, 60, 2354, 282, 1336, 100, 1254, 366, 419, 498, 483, 778, 1204, 292, 373, 845, 838, 1118, 2120, 815, 2616, 686, 1195, 745, 1112, 2132, 1588, 754, 1227, 1279, 1661, 716, 2275, 784, 2341, 1874, 1463, 1122, 2800, 1350, 1613, 2279, 1557, 1532

Offset: 1

T. D. Noe, Nov 06 2007

nonn

Such a sequence has finite length when the k-th term becomes greater than k.

The term a(2) = 0 is only conjectural - see A005185. a(4) = 0 is a theorem of Balamohan et al. (2007). - N. J. A. Sloane, Nov 07 2007, Apr 18 2014.

			a(1) = 6: the f-sequence is defined by f(1) = 1, f(n) = 2f(n-f(n-1)), which gives 1,2,2,4,2,8 but f(7) = 2f(-1) is undefined, so the length is 6.

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
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.
D. R. Hofstadter, Graph of first 21500 terms.
Index entries for Hofstadter-type sequences

Cf. A005185, A046700, A063882, A132172, A134679 (sequences for n=2..6).
See A240810 for another version.
A diagonal of the triangle in A240813.

Table[Clear[a]; a[n_] := a[n] = If[n<=k, 1, a[n-a[n-1]]+a[n-a[n-k]]]; t={1}; n=2; While[n<10000 && a[n-1]

A240816 Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = index of first nonexisting term 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.

Original entry on oeis.org

7, 0, 15, 165, 55, 14, 0, 0, 11, 12, 61, 38, 12, 13, 14, 2355, 31, 14, 14, 15, 16, 283, 64, 45, 15, 16, 18, 19, 1337, 369, 32, 16, 18, 19, 20

Offset: 1

N. J. A. Sloane, Apr 15 2014

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

Apart from the zero entries, equals A240813 + 1.

			Triangle begins:
     7;
     0,  15;
   165,  55, 14;
     0,   0, 11, 12;
    61,  38, 12, 13, 14;
  2355,  31, 14, 14, 15, 16;
   283,  64, 45, 15, 16, 18, 19;
  1337, 369, 32, 16, 18, 19, 20, ?;
  ...

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 A240810, A240814, A240815.

See A240813 for another version.

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

A134680 a(n) = length (or lifetime) 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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A240816 Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = index of first nonexisting term 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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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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