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Look-and-say sequence
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==== Conway's constant as a polynomial root ==== Conway's constant is the unique positive [[real root]] of the following [[polynomial]] {{OEIS|id=A137275}}: <math display="block">\begin{matrix} & &\qquad & &\qquad & &\qquad & & +1x^{71} & \\ -1x^{69} & -2x^{68} & -1x^{67} & +2x^{66} & +2x^{65} & +1x^{64} & -1x^{63} & -1x^{62} & -1x^{61} & -1x^{60} \\ -1x^{59} & +2x^{58} & +5x^{57} & +3x^{56} & -2x^{55} & -10x^{54} & -3x^{53} & -2x^{52} & +6x^{51} & +6x^{50} \\ +1x^{49} & +9x^{48} & -3x^{47} & -7x^{46} & -8x^{45} & -8x^{44} & +10x^{43} & +6x^{42} & +8x^{41} & -5x^{40} \\ -12x^{39} & +7x^{38} & -7x^{37} & +7x^{36} & +1x^{35} & -3x^{34} & +10x^{33} & +1x^{32} & -6x^{31} & -2x^{30} \\ -10x^{29} & -3x^{28} & +2x^{27} & +9x^{26} & -3x^{25} & +14x^{24} & -8x^{23} & & -7x^{21} & +9x^{20} \\ +3x^{19} & -4x^{18} & -10x^{17} & -7x^{16} & +12x^{15} & +7x^{14} & +2x^{13} & -12x^{12} & -4x^{11} & -2x^{10} \\ +5x^{9} & & +1x^{7} & -7x^{6} & +7x^{5} & -4x^{4} & +12x^{3} & -6x^{2} & +3x^{1} & -6x^{0} \\ \end{matrix} </math> This polynomial was correctly given in Conway's original ''Eureka'' article,<ref name="Conway-original-article" /> but in the reprinted version in the book edited by Cover and Gopinath<ref name="Conway-original-article" /> the term <math>x^{35}</math> was incorrectly printed with a minus sign in front.<ref> {{Cite book | last = Vardi | first = Ilan | title = Computational Recreations in Mathematica | publisher = [[Addison-Wesley]] | year = 1991 | isbn = 0-201-52989-0 }} </ref>
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