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

Author

Paolo Xausa, Jul 18 2024

Keywords

• nonn
• cons
• changed

Examples

			1.933184981899520446791424030335631586375183784479...
		

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, degree 5.

Crossrefs

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

Programs

Mathematica

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

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.