A191818 A sum-square avoiding sequence; fixed point of the map 0 -> 03; 1 -> 43; 3 -> 1; 4 -> 01.
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, 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, 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
Offset: 0
Keywords
Examples
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
References
- Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.
Links
- David A. Corneth, Table of n, a(n) for n = 0..10000
- Jean-Paul Allouche, Julien Cassaigne, Jeffrey Shallit, and Luca Q. Zamboni, A Taxonomy of Morphic Sequences, arXiv preprint arXiv:1711.10807[cs.FL], Nov 29 2017.
- J. Cassaigne, J. D. Currie, L. Schaeffer and Jeffrey Shallit, Avoiding Three Consecutive Blocks of the Same Size and Same Sum, arXiv:1106.5204 [cs.DM], 2011.
- Michel Rigo, Relations on words, arXiv preprint arXiv:1602.03364 [cs.FL], 2016.
Crossrefs
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.
Programs
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Mathematica
Nest[Flatten[# /. {0 -> {0, 3}, 1 -> {4, 3}, 3 -> 1, 4 -> {0, 1}}] &, 0, 9] (* Michael De Vlieger, Aug 03 2017 *) -
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
Formula
Fixed point of the map 0 -> 03; 1 -> 43; 3 -> 1; 4 -> 01.
Comments