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 A091579 Lengths of suffix blocks associated with A090822. 14
 1, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 67, 1, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 196, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 68, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 581, 3, 1, 9, 4, 25, 3, 1, 9, 4, 67, 1, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 196, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 68, 3, 1, 9, 4, 24, 1, 3, 1, 9, 4, 1731, 3, 1, 9, 4, 24 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The suffix blocks are what is called "glue string" in the paper by Gijswijt et al (2007). Roughly speaking, these are the terms >= 2 appended before the sequence (A090822) goes on with a(n+1) = 1 followed by all other initial terms a(2..n), cf. Example. The concatenation of these glue strings yields A091787. - M. F. Hasler, Aug 08 2018 LINKS Dion Gijswijt, Table of n, a(n) for n = 1..2000 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. EXAMPLE From M. F. Hasler, Aug 09 2018: In sequence A090822, after the initial (1, 1) follows the first suffix block or glue string (2) of length a(1) = 1. This is followed by A090822(4) = 1 which indicates that the suffix block has ended, and the whole sequence A090822(1..3) up to and including this suffix block is repeated: A090822(4..6) = A090822(1..3). Then A090822 goes on with (2, 2, 3, 1, ...), which tells that the second suffix block is A090822(7..9) = (2, 2, 3) of length a(2) = 3, whereafter the sequence starts over again: A090822(10..18) = A090822(1..9). (End) PROG (Python) # compute curling number of L def curl(L):     n = len(L)     m = 1 #max nr. of repetitions at the end     k = 1 #length of repeating block     while(k*(m+1) <= n):         good = True         i = 1         while(i <= k and good):             for t in range(1, m+1):                 if L[-i-t*k] != L[-i]:                     good = False             i = i+1         if good:             m = m+1         else:             k = k+1     return m # compute lengths of first n glue strings def A091579_list(n):     Promote = [1] #Keep track of promoted elements     L = [2]     while len(Promote) <= n:         c = curl(L)         if c < 2:             Promote = Promote+[len(L)+1]             c = 2         L = L+[c]     return [Promote[i+1]-Promote[i] for i in range(n)] # Dion Gijswijt, Oct 08 2015 CROSSREFS Cf. A090822, A091587 (records). For a smoothed version see A091839. Cf. A091787 for the concatenation of the glue strings. Sequence in context: A124573 A127550 A021317 * A136159 A005533 A331257 Adjacent sequences:  A091576 A091577 A091578 * A091580 A091581 A091582 KEYWORD nonn AUTHOR N. J. A. Sloane, Mar 05 2004 STATUS approved

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Last modified September 20 14:44 EDT 2021. Contains 347586 sequences. (Running on oeis4.)