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A374751 Decimal expansion of the third smallest univoque Pisot number.

%I A374751 #18 Sep 03 2025 04:25:40
%S A374751 1,9,0,5,1,6,6,1,6,7,7,5,4,0,1,8,9,0,9,5,7,2,7,8,7,8,3,0,3,6,4,0,1,5,
%T A374751 7,9,3,5,0,6,9,6,9,6,4,9,2,9,8,1,0,5,1,8,5,0,6,4,9,1,3,4,9,5,4,2,3,1,
%U A374751 0,7,6,4,2,7,7,7,0,8,5,9,4,3,4,5,0,4,1,3,7,7
%N A374751 Decimal expansion of the third smallest univoque Pisot number.
%C A374751 This number is denoted by Allouche et al. (2007) as chi. It's the unique Pisot number of degree 4 which is univoque (see Remark 4.1, p. 1646), and the smallest limit point of univoque Pisot numbers (see Theorem 5.3, p. 1651).
%H A374751 Paolo Xausa, <a href="/A374751/b374751.txt">Table of n, a(n) for n = 1..10000</a>
%H A374751 Jean-Paul Allouche, Christiane Frougny, and Kevin G. Hare, <a href="https://doi.org/10.1090/S0025-5718-07-01961-8">On Univoque Pisot Numbers</a>, Mathematics of Computation, Vol. 76, No. 259, July 2007, pp. 1639-1660 (<a href="https://doi.org/10.48550/arXiv.math/0610681">arXiv version</a>).
%H A374751 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PisotNumber.html">Pisot Number</a>.
%H A374751 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pisot%E2%80%93Vijayaraghavan_number">Pisot-Vijayaraghavan number</a>.
%H A374751 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>.
%F A374751 Equals the real root > 1 of x^4 - x^3 - 2*x^2 + 1.
%e A374751 1.905166167754018909572787830364015793506969649298...
%t A374751 First[RealDigits[Root[#^4 - #^3 - 2*#^2 + 1 &, 2], 10, 100]]
%Y A374751 Cf. A127583 (smallest), A374750 (second smallest), A374752.
%K A374751 nonn,cons,changed
%O A374751 1,2
%A A374751 _Paolo Xausa_, Jul 18 2024