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A267033 Decimal expansion of 4*arctan(sqrt(2)/5)-Pi/3. 3
0, 5, 5, 3, 7, 3, 6, 4, 5, 6, 6, 8, 4, 6, 3, 8, 6, 9, 7, 3, 0, 0, 7, 3, 8, 4, 1, 8, 3, 5, 7, 5, 0, 8, 5, 7, 8, 0, 1, 9, 7, 8, 1, 2, 4, 2, 5, 5, 3, 2, 2, 1, 1, 8, 7, 2, 5, 0, 8, 5, 9, 5, 3, 2, 6, 5, 7, 1, 5, 6, 0, 5, 5, 3, 5, 0, 4, 8, 8, 6, 3, 6, 5, 4, 0, 9, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Hales' constant used in his proof of the Kepler conjecture (Def. 1.6).
LINKS
Thomas C. Hales, A proof of the Kepler conjecture. In: Annals of Mathematics 162 (2005), nr. 3, p. 1065-1185.
FORMULA
Equals 4*arctan(sqrt(2)/5)-Pi/3.
Equals sqrt(2)*A267040-Pi/3.
Equals -sqrt(8)*A266814+2*Pi/3.
EXAMPLE
0.0553736456...
MATHEMATICA
len = 86; PadLeft[First@ #, len + Last@ Abs@ #] &@ RealDigits@ N[4 ArcTan[Sqrt[2]/5] - Pi/3, len] (* Michael De Vlieger, Jan 09 2016 *)
RealDigits[4*ArcTan[Sqrt[2]/5] - Pi/3, 10, 100][[1]] (* G. C. Greubel, Aug 19 2018 *)
PROG
(PARI) 4*atan(sqrt(2)/5) - Pi/3 \\ G. C. Greubel, Aug 19 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 4*Arctan(Sqrt(2)/5) - Pi(R)/3; // G. C. Greubel, Aug 19 2018
CROSSREFS
Sequence in context: A199617 A195693 A232813 * A306982 A278928 A273826
KEYWORD
nonn,cons
AUTHOR
Martin Renner, Jan 09 2016
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)