A Slow-Growing Sequence Defined by an Unusual Recurrence

نویسندگان

  • Fokko J. van de Bult
  • Dion C. Gijswijt
  • John P. Linderman
  • N. J. A. Sloane
  • Allan R. Wilks
چکیده

The sequence starts with a(1) = 1; to extend it one writes the sequence so far as XY , where X and Y are strings of integers, Y is nonempty and k is as large as possible: then the next term is k. The sequence begins 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, . . . A 4 appears for the first time at position 220, but a 5 does not appear until about position 1010 23 . The main result of the paper is a proof that the sequence is unbounded. We also present results from extensive numerical investigations of the sequence and of certain derived sequences, culminating with a heuristic argument that t (for t = 5, 6, . . .) appears for the first time at about position All correspondence should be directed to this author.

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تاریخ انتشار 2006