A374751 - OEIS

%I #15 Jul 19 2024 02:26:41

%S 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 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 0,7,6,4,2,7,7,7,0,8,5,9,4,3,4,5,0,4,1,3,7,7

%N Decimal expansion of the third smallest univoque Pisot number.

%C 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 Paolo Xausa, <a href="/A374751/b374751.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PisotNumber.html">Pisot Number</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pisot%E2%80%93Vijayaraghavan_number">Pisot-Vijayaraghavan number</a>.

%H <a href="/index/Al#algebraic">Index entries for algebraic numbers</a>.

%F Equals the real root > 1 of x^4 - x^3 - 2*x^2 + 1.

%e 1.905166167754018909572787830364015793506969649298...

%t First[RealDigits[Root[#^4 - #^3 - 2*#^2 + 1 &, 2], 10, 100]]

%Y Cf. A127583 (smallest), A374750 (second smallest), A374752.

%K nonn,cons

%O 1,2

%A _Paolo Xausa_, Jul 18 2024