A374751 Decimal expansion of the third smallest univoque Pisot number.

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

Offset: 1

Author

Paolo Xausa, Jul 18 2024

Keywords

• nonn
• cons
• changed

Comments

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).

Examples

			1.905166167754018909572787830364015793506969649298...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Jean-Paul Allouche, Christiane Frougny, and Kevin G. Hare, On Univoque Pisot Numbers, Mathematics of Computation, Vol. 76, No. 259, July 2007, pp. 1639-1660 (arXiv version).
• Eric Weisstein's World of Mathematics, Pisot Number.
• Wikipedia, Pisot-Vijayaraghavan number.
• Index entries for algebraic numbers, degree 4.

Crossrefs

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

Programs

Mathematica

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

Formula

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