This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A093370 #23 Jun 14 2025 17:15:23 %S A093370 0,1,2,5,10,22,44,91,182,369,738,1486,2972,5962,11924,23884,47768, %T A093370 95607,191214,382568,765136,1530552,3061104,6122765,12245530,24492171, %U A093370 48984342,97970902,195941804,391888040 %N 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. %H A093370 F. J. van de Bult, D. C. Gijswijt, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Sloane/sloane55.html">A Slow-Growing Sequence Defined by an Unusual Recurrence</a>, J. Integer Sequences, Vol. 10 (2007), #07.1.2. %H A093370 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 [<a href="http://neilsloane.com/doc/gijs.pdf">pdf</a>, <a href="http://neilsloane.com/doc/gijs.ps">ps</a>]. %H A093370 B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="http://arxiv.org/abs/1212.6102">On Curling Numbers of Integer Sequences</a>, arXiv:1212.6102 [math.CO], Dec 25 2012. %H A093370 B. Chaffin, J. P. Linderman, N. J. A. Sloane and Allan Wilks, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Sloane/sloane3.html">On Curling Numbers of Integer Sequences</a>, Journal of Integer Sequences, Vol. 16 (2013), Article 13.4.3. %H A093370 <a href="/index/Ge#Gijswijt">Index entries for sequences related to Gijswijt's sequence</a> %H A093370 <a href="/index/Cu#curling_numbers">Index entries for sequences related to curling numbers</a> %F A093370 Equals A121880(n)/2, or 2^(n-1) - A122536(n)/2. %F A093370 a(n)/2^(n-1) seems to converge to a number around 0.73. %e A093370 For n=2 there are 2 starting strings, 22 and 23 and only the first has k > 1. %e A093370 For n=4 there are 8 starting strings, but only 5 have k > 1, namely 2222, 2233, 2322, 2323, 2333. %Y A093370 Cf. A090822, A093369, A093371, A121880, A122536. %K A093370 nonn %O A093370 1,3 %A A093370 _N. J. A. Sloane_, Apr 28 2004 %E A093370 More terms from _Sarah Nibs_, via A122536, Sep 18 2006