A279037 Decimal expansion of the total area of Ford circles.

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

Table of n, a(n) for n=0..106.

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

Cf. A000010, A002117, A013662.

Sequence in context: A124473 A011108 A331370 * A328895 A154846 A173598

Adjacent sequences: A279034 A279035 A279036 * A279038 A279039 A279040

Keyword

nonn,cons

Author

Jean-François Alcover, Dec 04 2016

Status

approved