A246727 Decimal expansion of r_5, the 5th smallest radius < 1 for which a compact packing of the plane exists, with disks of radius 1 and r_5.

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

Offset: 0

Author

Jean-François Alcover, Sep 02 2014

Keywords

• nonn
• cons
• easy

Examples

			0.3861061048585385422861371299469896994436146884586173...
		

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2021, p. 73.
• Index entries for algebraic numbers, degree 4.

Crossrefs

Cf. A246723 (r_1), A246724 (r_2), A246725 (r_3), A246726 (r_4), A002193 (r_6 = sqrt(2)-1), A246728 (r_7), A246729 (r_8), A246730 (r_9).

Programs

Mathematica

RealDigits[Root[9x^4 - 12x^3 - 26x^2 - 12x + 9, x, 1], 10, 104] // First

PARI

(1 + 2*sqrt(3) - 2*sqrt(1 + sqrt(3)))/3 \\ Charles R Greathouse IV, Feb 10 2025

Formula

1st root of 9x^4 - 12x^3 - 26x^2 - 12x + 9.

Equals (1 + 2*sqrt(3) - 2*sqrt(1 + sqrt(3)))/3. - Amiram Eldar, Mar 27 2022