A246723 Decimal expansion of r_1, the smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_1.

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

Offset: 0

Author

Jean-François Alcover, Sep 02 2014

Keywords

• nonn
• cons
• easy

Examples

			0.101020514433643803605431850588217216068105038686659743...
		

Links

• Steven R. Finch, Errata and Addenda to Mathematical Constants, arXiv:2001.00578 [math.HO], 2020-2021, p. 62.
• Gabriel Klambauer, Summation of Series, Amer. Math. Monthly, Vol. 87, No. 2 (Feb., 1980), pp. 128-130.
• Wikipedia, Engel expansion
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A246724 (r_2), A246725 (r_3), A246726 (r_4), A246727 (r_5), A002193 (r_6 = sqrt(2)-1), A246728 (r_7), A246729 (r_8), A246730 (r_9).

Programs

Mathematica

RealDigits[5 - 2*Sqrt[6], 10, 104] // First

Formula

Equals 5 - 2*sqrt(6).

Equals Sum_{k>=1} binomial(2*k,k)/((k+1) * 12^k). - Amiram Eldar, Oct 04 2021

Engel expansion of 5 - 2*sqrt(6) = 1/10 + 1/(10*98) + 1/(10*98*9602) + ..., where [10, 98, 9602, ...] = A135927. See Klambauer, p. 130. - Peter Bala, Feb 01 2022

Equals exp(-arccosh(5)). - Amiram Eldar, Jul 06 2023