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A246723
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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.
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9
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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
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OFFSET
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0,5
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LINKS
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Gabriel Klambauer, Summation of Series, Amer. Math. Monthly, Vol. 87, No. 2 (Feb., 1980), pp. 128-130.
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FORMULA
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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
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EXAMPLE
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0.101020514433643803605431850588217216068105038686659743...
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MATHEMATICA
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RealDigits[5 - 2*Sqrt[6], 10, 104] // First
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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