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 A191818 #48 May 27 2025 07:28:51
%S A191818 0,3,1,4,3,0,1,1,0,3,4,3,4,3,0,3,1,0,1,1,0,1,1,0,3,1,4,3,0,3,4,3,4,3,
%T A191818 0,3,4,3,4,3,0,3,1,4,3,0,1,1,0,3,1,0,1,1,0,1,1,0,3,1,0,1,1,0,1,1,0,3,
%U A191818 1,4,3,0,1,1,0,3,4,3,4,3,0,3,1,4,3,0,3,4,3,4,3,0,3,4,3,4,3,0,3,1
%N A191818 A sum-square avoiding sequence; fixed point of the map 0 -> 03; 1 -> 43; 3 -> 1; 4 -> 01.
%C A191818 A "sum square" means two consecutive blocks of the same length and same sum.
%C A191818 This is a pure primitive morphic sequence. - _N. J. A. Sloane_, Jul 14 2018
%D A191818 Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.
%H A191818 David A. Corneth, <a href="/A191818/b191818.txt">Table of n, a(n) for n = 0..10000</a>
%H A191818 Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, and Luca Q. Zamboni, <a href="https://arxiv.org/abs/1711.10807">A Taxonomy of Morphic Sequences</a>, arXiv preprint arXiv:1711.10807[cs.FL], Nov 29 2017.
%H A191818 J. Cassaigne, J. D. Currie, L. Schaeffer and Jeffrey Shallit, <a href="http://arxiv.org/abs/1106.5204">Avoiding Three Consecutive Blocks of the Same Size and Same Sum</a>, arXiv:1106.5204 [cs.DM], 2011.
%H A191818 Michel Rigo, <a href="http://arxiv.org/abs/1602.03364">Relations on words</a>, arXiv preprint arXiv:1602.03364 [cs.FL], 2016.
%F A191818 Fixed point of the map 0 -> 03; 1 -> 43; 3 -> 1; 4 -> 01.
%e A191818 Start with 0 which maps to 03, then concatenate the image of the second digit, 3, which is 1, so we have 031. Then concatenate the image of the third digit, 1, which is 43. We then have 03143. Etc. - _David A. Corneth_, Aug 03 2017
%t A191818 Nest[Flatten[# /. {0 -> {0, 3}, 1 -> {4, 3}, 3 -> 1, 4 -> {0, 1}}] &, 0, 9] (* _Michael De Vlieger_, Aug 03 2017 *)
%o A191818 (PARI) first(n) = {my(res = [0,3], i = 2, m = Map(Mat([0, [0, 3]; 1, [4, 3]; 3, [1]; 4,[0, 1]]))); while(#res < n, res = concat(res, mapget(m, res[i])); i++);res} \\ _David A. Corneth_, Aug 03 2017
%Y A191818 Sequences mentioned in the Allouche et al. "Taxonomy" paper, listed by example number: 1: A003849, 2: A010060, 3: A010056, 4: A020985 and A020987, 5: A191818, 6: A316340 and A273129, 18: A316341, 19: A030302, 20: A063438, 21: A316342, 22: A316343, 23: A003849 minus its first term, 24: A316344, 25: A316345 and A316824, 26: A020985 and A020987, 27: A316825, 28: A159689, 29: A049320, 30: A003849, 31: A316826, 32: A316827, 33: A316828, 34: A316344, 35: A043529, 36: A316829, 37: A010060.
%K A191818 nonn
%O A191818 0,2
%A A191818 _Jeffrey Shallit_, Jun 28 2011