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A279037
Decimal expansion of the total area of Ford circles.
0
8, 7, 2, 2, 8, 4, 0, 4, 1, 0, 6, 5, 6, 2, 7, 9, 7, 6, 1, 7, 5, 1, 9, 7, 5, 3, 2, 1, 7, 1, 2, 2, 5, 8, 7, 0, 6, 4, 0, 2, 7, 7, 7, 8, 0, 8, 8, 9, 9, 3, 3, 0, 3, 2, 5, 2, 0, 3, 5, 2, 1, 4, 7, 7, 8, 4, 9, 8, 5, 5, 8, 2, 7, 7, 6, 4, 5, 4, 2, 4, 3, 6, 1, 6, 6, 5, 4, 2, 2, 2, 8, 6, 2, 8, 9, 7, 9, 8, 5, 5, 9, 5, 9, 8, 8, 7, 8
OFFSET
0,1
COMMENTS
Named after the American mathematician Lester Randolph Ford, Sr. (1886-1967). - Amiram Eldar, Jun 24 2021
LINKS
L. R. Ford, Fractions, The American Mathematical Monthly, Vol. 45, No. 9 (1938), pp. 586-601.
Wieslaw Marszalek, Circuits with Oscillatory Hierarchical Farey Sequences and Fractal Properties, Circuits Syst Signal Process, Vol. 31 (2012), pp. 1279-1296.
Eric Weisstein's World of Mathematics, Ford Circle.
Wikipedia, Ford circle.
FORMULA
Equals (Pi/4) * Sum_{n >= 1} EulerPhi(n)/n^4.
Equals (Pi/4) * zeta(3)/zeta(4).
Equals 45*zeta(3) / (2*Pi^3).
EXAMPLE
0.8722840410656279761751975321712258706402777808899330325203521...
MATHEMATICA
RealDigits[Pi/4 * Zeta[3]/Zeta[4], 10, 107][[1]]
PROG
(PARI) Pi/4 * zeta(3)/zeta(4) \\ Michel Marcus, Dec 04 2016
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved