A374752 Decimal expansion of phi_4, a limit point of the set of Pisot numbers in (1,2).

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

Offset

1,2

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).

Kevin G. Hare and Nikita Sidorov, Conjugates of Pisot numbers, International Journal of Number Theory, Vol. 17, No. 06 (2021), pp. 1307-1321 (arXiv version).

Eric Weisstein's World of Mathematics, Pisot Number.

Wikipedia, Pisot-Vijayaraghavan number.

Index entries for algebraic numbers.

Formula

Equals the real root of x^5 - 2*x^4 + x - 1.

Using the notation of Hare and Sidorov (2021, see Theorem 3.1), phi_1 = psi_1 (A001622) < phi_2 (A109134) < psi_2 (A058265) < phi_3 (A275828) < chi (A374751) < psi_3 (A086088) < phi_4 (this constant) < ... < psi_r < phi_(r+1) < ... < 2.

Example

1.933184981899520446791424030335631586375183784479...

Mathematica

First[RealDigits[Root[#^5 - 2*#^4 + # - 1 &, 1], 10, 100]]

Crossrefs

Cf. A001622, A058265, A086088, A109134, A275828, A374751.

Sequence in context: A021842 A363848 A011112 * A138064 A063569 A037921

Adjacent sequences: A374749 A374750 A374751 * A374753 A374754 A374755

Keyword

nonn,cons

Author

Paolo Xausa, Jul 18 2024

Status

approved