A246726 Decimal expansion of r_4, the 4th smallest radius < 1 for which a compact packing of the plane exists, with disks of radius 1 and r_4.

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

Offset: 0

Author

Jean-François Alcover, Sep 02 2014

Keywords

• nonn
• cons
• easy

Examples

			0.3491981862085498764736232370456943152782620498437475...
		

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), A246727 (r_5), A002193 (r_6 = sqrt(2)-1), A246728 (r_7), A246729 (r_8), A246730 (r_9).

Cf. A214726.

Programs

Mathematica

RealDigits[Root[x^4 - 28x^3 - 10x^2 + 4x + 1, x, 3], 10, 103] // First

Formula

3rd root of x^4 - 28x^3 - 10x^2 + 4x + 1.

Equals 1/(cosec(Pi/12)-1) = 1/(A214726 - 1). - Amiram Eldar, Mar 27 2022