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

1,2

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).

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.

Formula

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

Example

1.905166167754018909572787830364015793506969649298...

Mathematica

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

Crossrefs

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

Sequence in context: A309605 A010770 A021921 * A247718 A154399 A195483

Adjacent sequences: A374748 A374749 A374750 * A374752 A374753 A374754

Keyword

nonn,cons

Author

Paolo Xausa, Jul 18 2024

Status

approved