

A191818


A sumsquare avoiding sequence; fixed point of the map 0 > 03; 1 > 43; 3 > 1; 4 > 01.


25



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
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OFFSET

0,2


COMMENTS

A "sum square" means two consecutive blocks of the same length and same sum.


REFERENCES

Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence  see "List of Sequences" in Vol. 2.


LINKS



FORMULA

Fixed point of the map 0 > 03; 1 > 43; 3 > 1; 4 > 01.


EXAMPLE

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


MATHEMATICA

Nest[Flatten[# /. {0 > {0, 3}, 1 > {4, 3}, 3 > 1, 4 > {0, 1}}] &, 0, 9] (* Michael De Vlieger, Aug 03 2017 *)


PROG

(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


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.


KEYWORD

nonn


AUTHOR



STATUS

approved



