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 A093370 Start with any initial string of n numbers s(1), ..., s(n), with s(1) = 2, other s(i)'s = 2 or 3 (so there are 2^(n-1) starting strings). The rule for extending the string is this as follows: To get s(n+1), write the string s(1)s(2)...s(n) as xy^k for words x and y (where y has positive length) and k is maximized, i.e., k = the maximal number of repeating blocks at the end of the sequence. Then a(n) = number of starting strings for which k > 1. 8
 0, 1, 2, 5, 10, 22, 44, 91, 182, 369, 738, 1486, 2972, 5962, 11924, 23884, 47768, 95607, 191214, 382568, 765136, 1530552, 3061104, 6122765, 12245530, 24492171, 48984342, 97970902, 195941804, 391888040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Table of n, a(n) for n=1..30. 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]. B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, arXiv:1212.6102 [math.CO], Dec 25 2012. B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, On Curling Numbers of Integer Sequences, Journal of Integer Sequences, Vol. 16 (2013), Article 13.4.3. Index entries for sequences related to Gijswijt's sequence Index entries for sequences related to curling numbers FORMULA Equals A121880(n)/2, or 2^(n-1) - A122536(n)/2. a(n)/2^(n-1) seems to converge to a number around 0.73. EXAMPLE For n=2 there are 2 starting strings, 22 and 23 and only the first has k > 1. For n=4 there are 8 starting strings, but only 5 have k > 1, namely 2222, 2233, 2322, 2323, 2333. CROSSREFS Cf. A090822, A093369, A093371, A121880, A122536. Sequence in context: A073777 A215422 A026633 * A372957 A094537 A135098 Adjacent sequences: A093367 A093368 A093369 * A093371 A093372 A093373 KEYWORD nonn AUTHOR N. J. A. Sloane, Apr 28 2004 EXTENSIONS More terms from Guy P. Srinivasan, via A122536, Sep 18 2006 STATUS approved

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Last modified August 12 02:57 EDT 2024. Contains 375085 sequences. (Running on oeis4.)