A094321 a(1) = 2. For n>1, let k = largest integer such that the word a(1)a(2)...a(n-1) is of the form xy^k for words x and y (where y has positive length), i.e., the maximal number of repeating blocks at the end of the sequence so far. If k>1, a(n) = k. If k=1, choose a(n) so that the next k (that for a(1),...,a(n)) is as large as possible and if there is more than one choice for this a(n), pick the smallest.

2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 4, 4, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2

Offset

1,1

Comments

Resembles A091787, but constructed by a greedy algorithm.

Links

Table of n, a(n) for n=1..99.

F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence, J. Integer Sequences, Vol. 10 (2007), #07.1.2.

F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, A Slow-Growing Sequence Defined by an Unusual Recurrence [pdf, ps].

Index entries for sequences related to Gijswijt's sequence

Example

For n=2: we have a(1) = 1, so k=1; taking a(2) = 2 makes the next k=2.
For n=3, we have a(1),a(2) = 22, so k = 2 = a(3).
For n=4, we have a(1),...,a(3) = 222, so k = 3 = a(4).
For n=5, we have a(1),...,a(4) = 2223, so k = 1; taking a(5) = 3 makes the next k=2.
For n=6, we have a(1),...,a(5) = 22233, so k = 2 = a(6); etc.

Crossrefs

Cf. A091787, A090822.

Sequence in context: A308890 A081414 A328577 * A107789 A124064 A348470

Adjacent sequences: A094318 A094319 A094320 * A094322 A094323 A094324

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 03 2004

Extensions

More terms from John P. Linderman, Jun 03 2004

Status

approved